In the end I'm ending with something like this(very raw code so far, but enought for those who's seaching for solution. You need php google spreadsheet client of https://github.com/asimlqt/php-google-spreadsheet-client). Thats tiny example of inserting one row to my spreadsheet (sorry about my code, but showing just working example)
Thanks for bram brambring showing better way to authorization - answer by bram brambring
<?php
/*
 * Google Spreadsheet class to work with google spreadsheets obviously ;D [using OAuth 2.0, as Zend Gdata is not anymore working]
 */
require_once('/Google/Spreadsheet/ServiceRequestInterface.php');
require_once('/Google/Spreadsheet/DefaultServiceRequest.php');
require_once('/Google/Spreadsheet/ServiceRequestFactory.php');
require_once('/Google/Spreadsheet/Spreadsheet.php');
require_once('/Google/Spreadsheet/SpreadsheetFeed.php');
require_once('/Google/Spreadsheet/SpreadsheetService.php');
require_once('/Google/Spreadsheet/Exception.php');
require_once('/Google/Spreadsheet/UnauthorizedException.php');
require_once('/Google/Spreadsheet/Spreadsheet.php');
require_once('/Google/Spreadsheet/Util.php');
require_once('/Google/Spreadsheet/Worksheet.php');
require_once('/Google/Spreadsheet/WorksheetFeed.php');
require_once('/Google/Spreadsheet/ListFeed.php');
require_once('/Google/Spreadsheet/ListEntry.php');
require_once('/Google/Spreadsheet/CellFeed.php');
require_once('/Google/Spreadsheet/CellEntry.php');
require_once('/Google/Config.php');
require_once('/Google/Client.php');
require_once('/Google/Auth/Abstract.php');
require_once('/Google/Auth/OAuth2.php');
require_once('/Google/Http/Request.php');
require_once('/Google/Utils.php');
require_once('/Google/IO/Abstract.php');
require_once('/Google/IO/Curl.php');
require_once('/Google/Http/CacheParser.php');
require_once('/Google/Logger/Abstract.php');
require_once('/Google/Logger/Null.php');
require_once('/Google/Exception.php');
require_once('/Google/Auth/Exception.php');
require_once('/Google/Auth/AssertionCredentials.php');
require_once('/Google/Cache/Abstract.php');
require_once('/Google/Cache/File.php');
require_once('/Google/Signer/Abstract.php');
require_once('/Google/Signer/P12.php');
use Google\Spreadsheet\DefaultServiceRequest;
use Google\Spreadsheet\ServiceRequestFactory;
class Google_Spreadsheet
{
    private $default = array(
        'worksheetCols' => 12,
        'worksheetRows' => 25
    );
    private $spreadsheetKey;
    private $spreadsheetName;
    private $worksheetName;
    private $spreadsheetFeed;
    public $initialized = true;
    public function __construct($spreadsheetKey, $worksheetName, $spreadsheetName = '')
    {
        $this->spreadsheetKey = $spreadsheetKey;
        $this->worksheetName = $worksheetName;
        $this->spreadsheetName = $spreadsheetName;
        $this->initialized = $this->initialize();
        return true;
    }
    private function getToken() {
        $client_email = '318977712937456456454656563tcfjblgoi@developer.gserviceaccount.com';
        $private_key = file_get_contents('API Project-f10e456456b60.p12');
        $scopes = array('https://spreadsheets.google.com/feeds');
        $credentials = new Google_Auth_AssertionCredentials(
            $client_email,
            $scopes,
            $private_key,
            'notasecret',                                 // Default P12 password
            'http://oauth.net/grant_type/jwt/1.0/bearer' // Default grant type
        );
        $client = new Google_Client();
        $client->setAssertionCredentials($credentials);
        if ($client->getAuth()->isAccessTokenExpired()) {
            $client->getAuth()->refreshTokenWithAssertion();
        }
        $tokenData = json_decode($client->getAccessToken());
        return $tokenData->access_token;
    }
    public function initialize(/*$reInitialized = false*/)
    {
        // load OAuth2 token data - exit if false
        $tokenData = $this->getToken();
        $serviceRequest = new DefaultServiceRequest($tokenData);
        ServiceRequestFactory::setInstance($serviceRequest);
        $spreadsheetService = new Google\Spreadsheet\SpreadsheetService();
        try {
            $spreadsheetFeed = $spreadsheetService->getSpreadsheets();
        } catch (\Google\Spreadsheet\UnauthorizedException $e) {    
            Google_Spreadsheet::warnAdmin($e->getMessage());
            return false;
        }
        $this->spreadsheetFeed = $spreadsheetFeed;
        return true;
    }
    public function insertRow($rowData, $default_fields = array()) {
        $spreadsheetFeed = $this->spreadsheetFeed;
        $spreadsheet = $this->spreadsheetKey ? $spreadsheetFeed->getByKey($this->spreadsheetKey) : $spreadsheetFeed->getByTitle($this->spreadsheetName);
        if(!$spreadsheet && !empty($this->spreadsheetName)) {
            $spreadsheet = $spreadsheetFeed->getByTitle($this->spreadsheetName);
        }
        if(!$spreadsheet) {
            Google_Spreadsheet::warnAdmin('No spreadsheet', serialize($rowData));
            return false;
        }
        $worksheetFeed = $spreadsheet->getWorksheets();
        $worksheet = $worksheetFeed->getByTitle($this->worksheetName);
        if(!$worksheet) {
            //create worksheet if not exist
            $worksheet = $spreadsheet->addWorksheet($this->worksheetName, $this->default['worksheetRows'], $this->default['worksheetCols']);
            $cellFeed = $worksheet->getCellFeed();
            for( $i= 1 ; $i <= $this->default['worksheetCols']; $i++ ) {
                if(isset($default_fields[$i])) {
                    $cellFeed->editCell(1, $i, $default_fields[$i]);
                }
                else {
                    $cellFeed->editCell(1, $i, "head");
                }
                $cellFeed->editCell(2,$i,"content");
            }
        }
        if(!$worksheet) {
            Google_Spreadsheet::warnAdmin('No worksheet', serialize($rowData));
            return false;
        }
        $listFeed = $worksheet->getListFeed();
        $data = array();
        foreach ($listFeed->getEntries() as $entry) {
            $values = $entry->getValues();
            $data[] = $values;
            break; //only first row needed, as we need keys
        }
        $keys = array();
        if(!count($data)) {
            Google_Spreadsheet::warnAdmin('No data', serialize($rowData));
            return false;
        }
        foreach ($data[0] as $key => $value) {
            $keys[] = $key;
        }
        $newRow = array();
        $count = 0;
        foreach($keys as $key) {
            if(isset($rowData[$count])) {
                $newRow["$key"] = $rowData[$count];
            }
            else {
                $newRow["$key"] = '';
            }
            $count++;
        }
        $listFeed->insert($newRow);
        return true;
    }
    static function warnAdmin($reason = '', $content = '') {
        //temporal function to warn myself about all the stuff happening wrong :)
    }
}
And in main model I'm using:
$spreadsheet = new Google_Spreadsheet("spreadsheet name or ID", $worksheetname, "My spreadsheet name");
        if(!$spreadsheet->initialized) {
            Google_Spreadsheet::warnAdmin('cannot initialize spreadsheet', serialize($rowValues));
        }
        if(!$spreadsheet->initialized || !$spreadsheet->insertRow($rowValues, $this->default_fields)) {
            Google_Spreadsheet::warnAdmin('failed to insert row ');
        }
@Edit, thanks to bram brambring for his token solution, seems more easier than my. Working like a charm now, I hope his way it gonna refresh token normally. THANK YOU DUDE!