Kenny Cunningham admitted he had no complaints with referee Chris Foy's decision to send him off after just 24 minutes at Highbury.
Blues' captain hauled down Freddie Ljungberg as he homed in on Maik Taylor to leave Birmingham with an uphill task for 66 minutes.
However, they almost grabbed a point due to the heroics of Maik Taylor before falling to a deflected Robin van Persie goal with just nine minutes remaining and Cunningham held his hands up as Birmingham were left with ten men for the third consecutive Premiership fixture.
"It was a fair decision," admitted the Republic of Ireland international. "I was looking across the pitch and I was the last man, so I can have no complaints.
"In hindsight it was a poor tackle and maybe it would have been better to stay on my feet and try to track his run. It was a bad tackle and, unfortunately, it has cost us.
"He was clever as he caught me out of the corner of his eye and he was clever enough just to touch the ball past me, as I had committed myself.
"But he was a little bit too quick for me and when I was halfway there I knew I wasn't going to reach him, but It is impossible to pull yourself back at that stage."
Birmingham had started in positive fashion and looked in charge for the opening 20 minutes and Emile Heskey was only denied by Ashley Cole's goal line clearance.
Despite Cunningham's dismissal, they still erected a thick blue wall that Arsenal struggled to pierce and Cunningham felt confident of claiming at least a point.
"Maik made some great saves and they were always going to pen us in with a man advantage. They had three or four great chances in the first half and that was a big time in the game because, if we had conceded then, perhaps they could have gone on to score three or four.
"The lads took a lot of heart and encouragement from that and it deflated Arsenal a little bit. I was watching the game from the tunnel in the second half and I really felt confident we could take something from the game.
"They had run out of ideas, gone a bit flat and we were looking solid and organised. It was only a speculative shot with the aid of a deflection that has cost us.
"It hit Stephen, as he dangled a foot and it took a bad dip towards Maik's body and bounced over him. It is difficult to blame anyone as Stephen did the right thing in trying to block the shot.
"We looked the more dangerous team for 20 minutes, as Jermaine looked bright down the right hand side and Emile was a big threat and had his chance was cleared off the line.
"You never know how the game would have panned out, but we feel as though we could really have posed a threat to Arsenal if we had kept 11 players on the pitch.
"You have to take positives and I think Stephen Clemence was outstanding for his first game back today, but everyone contributed."
Even Arsenal manager ArsEne Wenger agreed it was a lucky Arsenal winner.
"I'll take a scrappy goal like that if it wins the game. To be honest, I could not see any other kind of goal beating Taylor," he said of the Northern Ireland goalkeeper, performing in the presence of England coach Sven-G^ran Eriksson.
"He deserves a lot of credit. He was outstanding, and I'm sure Sven is glad he's not playing for Austria or Poland (in World Cup qualifiers) next week."
Wenger also concurred with the red card. "I didn't want to see a player sent off from the other side - even though I thought the decision was correct," he said. "I would have preferred 11 against 11."