The Swans boss expressed his delight at a morale-boosting victory but, amid comments from other managers, does not believe progressing the FA Cup will affect league chances
The 49-year-old saw goals from Wilfried Bony change the game as the Swans booked their place in the fifth round before turning attentions to a crucial league clash with Fulham on Tuesday.
Paul Lambert recently caused controversy by suggesting Aston Villa could "do without" the FA Cup yet, as Swansea continue their journey in the Europa League, Laudrup does not feel league form will suffer.
"A win always gives confidence but again this is another competition and that is one of the downsides to a team that is used to playing in so many competitions," he told reporters at his press-conference.
"In our case we are entering February and we’re still in three competitions. Is that good or bad? Personally I feel it’s good as it gives a lot of games and a lot of experience.
"But on the other hand it’s understandable that some people say that wouldn’t it be better to have one – the Premier League – to focus and concentrate on that.
"I can understand that point of view as well but I still feel it’s always better to win than to lose."
Meanwhile, Birmingham manager Lee Clark expressed his disappointment at the defeat having taken the lead through Lee Novak, admitting Swansea's quality in front of goal was the difference.
"We’re disappointed because we had it within our grasp," he said. "We had the chance to at least get a draw and a replay but we certainly had a right good chance of causing that upset.
"I think my players have done lots of very good things today. The difference between the players who operate at this level and the ones in the Championship is you don’t need three, four, five chances.
"They didn’t create lots of chances against us but they’ve finished two very accomplished finishes from Bony. He’s a player in very good form at the highest level of the game."