He said: "It was a bit of luck I suppose. It's a bit of a lottery, penalties, for goalkeepers, and luckily today I've gone the right way and got a strong enough hand to get it away."
The spot-kick, for Nigel de Jong's handball, was the first awarded against City this season, and Given quipped: "I hope it's the last as well!
"It probably was a penalty looking back, I think Nigel's hand was a bit high and it was the right decision from the referee.
"Luckily for us we've managed to keep it out and we've kept a clean sheet. I think we can play better than we did today and we'll take a point."
But he continued: "We're disappointed, these are games where we're looking to pick up three points.
"Credit to Birmingham, they had good spirit today and a good workrate in their team. It's a hard enough place to come, they won last week and I suppose they took a lot of confidence from that.
"But we were coming here today looking for three points, and the same against Fulham last week when we threw away a two-goal lead, so we've been disappointed in the last couple of weeks."
Birmingham boss Alex McLeish was also frustrated by the outcome after his side created a host of chances, only to be kept at bay by Given.
"We're disappointed in there (the dressing room) not to have three points, and that's a measure of how our team played today," he said.
"James McFadden again today looked very sharp supporting the front two but just perhaps lacked that bit of composure in front of goal. I'm hoping that will come, I think it will."
Scotland forward McFadden was withdrawn shortly after his miss from the spot, and his fellow countryman joked: "Yeah, it was a hopeless miss wasn't it? He deserved to come off after that!
"No, he was struggling a wee bit and maybe the fresh pair of legs in the end helped us - although maybe I jumped the gun a bit with James.
"He felt he could get better, but I thought 'how long is it going to take you to not limp any more?' I made the decision and it was a great team performance."
Barry Ferguson was needlessly sent off deep into injury time for impeding Pablo Zabaleta as the Argentinian took a throw-in, and McLeish admitted the experienced former Scotland captain should have known better.
"He should have, he's apologised to myself and his team-mates," he said.
"He'll be missing next week, which is disappointing because he's been exceptional.
"He had another influential game and it's disappointing to lose him, we can't afford the indiscipline over the season, especially with such a fragile squad, to go awry at any stage.
"Barry had a little rush of blood, maybe thought they could break up the park and score, but they had a lot to do from that situation."