Greg Abbott's charges succumbed to a 3-1 reversal at Brunton Park having taken a shock second-minute lead courtesy of an Ian Harte penalty.
The Cumbrians had lost their previous two league outings against Brighton and Oldham respectively without scoring a goal, but Thirlwell believes the club can take "a lot of positives" from their defeat to the Premier League strugglers.
"The lads put a good shift in and I think that's rightly so on the back of what happened last Saturday when we didn't produce or play as we normally can," he told the club's official website.
"We certainly brought a bit of pride back for ourselves and for the fans, despite the result, because of the type of performance that we gave.
"We couldn't have tried any harder and we can take a heck of a lot of positives out of it as we go into the Southampton game at the weekend."