Stewart moved to Meadow Lane ahead of Saturday's 1-0 defeat to fellow high-fliers Tranmere, which was County's second loss in as many matches following the defeat to Stevenage in midweek.
But the 30-year-old is confident his new team can bounce back against Carlisle this weekend.
"It's a great club with lots of good players and I've seen that everyone wants the ball," he told the club's official website.
"They want to pass the ball and even in the Championship some teams are more direct but I think it will stand us in good stead. Hopefully we can bounce back and I don't see no reason why the team can't get promoted this year.
"Sometimes defeats like this is when you learn the most about your team and about the players around you. We need to go into this weekend's game and try to correct the mistakes we've made. Hopefully we can progress and win more games."