The Gunners beat holders Wigan on penalties at the start of the month to reach their first major final since 2011.
Kallstrom believes that victory has helped the squad grow in confidence as they try to secure Champions League qualification.
"We had a couple of negative results during a couple of weeks and some games we were playing alright but didn't get the result," the Swede told the club's official website.
"The semi-final of the FA Cup turned everything around because you win a difficult game where we were struggling. In the end you get a positive result for everybody, the fans, the players. It gives you a confidence boost that is really good."
Arsenal return to action tonight (Monday) when they host Newcastle United in the Premier League.