I think regular expressions might be a way to go.
In VBA, you need to enable the reference to "Microsoft VBScript Regular Expressions 5.5". This question and its accepted answer has a detailed descrpition on what are Regular Expressions and how to enable them in your project (it's for Excel, but for Access is the same route).
Once you have the reference enabled, this little function will give you a "clean" string:
Public Function filterString(str As String)
    Dim re As RegExp, obj As Object, x As Variant, first As Boolean
    Set re = New RegExp
    With re
        .Global = True
        .IgnoreCase = True
        .MultiLine = False
        .Pattern = "SR_[0-9]" ' This will match the string "SR_" 
                              ' followed by a digit
    End With
    filterString = ""
    first = True
    If re.Test(str) Then
        Set obj = re.Execute(str)
        For Each x In obj
            If first Then
                first = False
            Else
                filterString = filterString & ";"
            End If
            filterString = filterString & x
        Next x
    End If
End Function
If you test it you'll see that the result is:
filterString("X_11;SR_4;D_11;SR_2")
  SR_4;SR_2
which is the result you want.
Now, a simple select query will give you what you need:
select filterString([Errors]) as err
from [yourTable]
where [yourTable].[Errors] like '*sr*'
Hope this helps