The Swedish midfielder, who is on loan from Spartak Moscow, came off the bench late on at the Emirates Stadium as the Gunners saw their Premier League title hopes suffer another blow.
However, Kallstrom was happy to get on the pitch after spending two months on the sidelines with a back injury.
"For me, it felt really good coming on. I had a lot of time with the ball, I had some clean passes. I was involved and I'm just pleased to be out there playing," he told the club's official website.
"It's exciting, and it's like a dream come true to play for Arsenal in the Premier League. I'm just unhappy my debut didn't end in a win. Everything felt good for me, obviously except their last goal and the last minutes of the match."
Arsenal continue their Premier League campaign on Saturday when they play host to Manchester City.