The Cumbrians took the lead through Hallam Hope in the first half but the Magpies rallied round and Ryan Yates struck back in the second half.
The result was a welcome boost after the 2-0 defeat at Crewe Alexandra in midweek and keeps Notts second in League Two with a tally of 30 points from 15 games.
"It was important to come away with something," he told the official Notts website. "The most important thing after a defeat is not to lose the next one.
"It's a good point because they are a good side and we're delighted with it, although it could have been three because we had some good chances in the second half, which we dominated.
"Ross Fitzsimons made some fantastic saves in the first half but I think we showed them a bit too much respect and we didn't get in amongst them.
"It was a great reaction in the second half and we fully deserved to get back into it. Even though we went 1-0 down, the players stuck in there and made it difficult for Carlisle so there are a lot of positives to take.
"We've got to respect the point because these are the ones which will mean a lot if we're going to be in and around it come the end of the season."
Share your thoughts about this news story on Pride of Nottingham by signing up to the website, visiting the forum and joining in the chat with hundreds of fellow Notts County fans.
Fancy showcasing your brand or business on Pride of Nottingham? Click here to find out more about sponsorship and advertising opportunities with us.