Create New Column based on Value found between Quotation Marks

quincy_p, here is my suggested solution.

I am using a test data table of one row with one column called [Integration_Result__c] which contains the full text of the error message you posted

Error CS_ServiceRequest_PUB.Create_ServiceRequest API Programming Error (CS_ServiceRequest_UTIL.Validate_Customer_Product): The value "111448692" for field p_customer_product_id is invalid.

I then created a Calculated Column with this DAX expression:

assetID = 
    VAR search1 = "(CS_ServiceRequest_UTIL.Validate_Customer_Product): The value """
    VAR search2 = """ for field p_customer_product_id is invalid"
    VAR pos1 = FIND(search1, YourTable[Integration_Result__c], 1, 0)
    VAR pos2 = FIND(search2, YourTable[Integration_Result__c], 1, 0)
    VAR assetID = 
        SWITCH(TRUE(),
            pos1 > 0 && pos2 > 0, 
            MID(
                YourTable[Integration_Result__c],
                pos1 + LEN(search1),
                pos2 - pos1 - LEN(search1)
            )
        )
    RETURN assetID

This gives me the following output:

Is this what you were looking for?