The Swede, who joined the club on loan from Spartak Moscow in January, played the full 90 minutes at the Emirates Stadium as the Gunners earned a 3-1 victory over their London rivals.
Having only recently returned from a back injury, Kallstrom is now happy to be playing his part for Arsene Wenger's side.
"It feels very good," he told Expressen. "It was fun to play, it was long since I did that.
"It was truly fun to get to play 90 minutes and terrific to win. It is obvious that it feels very good, you play together with very skilled players here.
"Of course, it feels good that you are starting to play your part. The more playing time you get, the easier it becomes to get into it."
Arsenal continue their quest for Champions League qualification on Sunday away to Hull City.