The Black Cats were two up inside an hour thanks to Darren Bent's penalty and an own goal from Stephen Carr, but Blues defenders Scott Dann and Liam Ridgewell netted in the final 12 minutes to earn the visitors a point.
Sunderland found themselves down to 10 men two minutes before half-time when new captain Lee Cattermole was shown a second yellow card for a foul on Lee Bowyer, but it was his first booking that really riled Bruce.
Taylor was taking charge of only his third Premier League game and Bruce described the 31-year-old as "out of his depth".
"The first yellow card, nobody in the ground knows what it's for," said the Sunderland boss.
"Cameron Jerome fell over and made a meal of it but apparently he hasn't booked him for that but for Catts kicking the ball away. I've seen it and he never kicked the ball away, he passed it to them.
"You could say Catts was naive on the second one but in my opinion the referee, I think it's his second or third game, he was out of his depth and if you're going to fast-track people through they have to be exceptional.
"I don't want to criticise referees but I think he's only been refereeing for four years and it looked like it.
"For it to be in a Premier League game, when we've got (fourth official) Chris Foy standing there, one of the best officials, it doesn't make sense. Today, all the big decisions, in my opinion, he got them wrong."
Cattermole was involved in another contentious incident when he caught Birmingham striker Garry O'Connor with an elbow, causing a nasty cut above the Scot's eye.
Blues boss Alex McLeish was unhappy with the challenge, saying: "The guy's jumped with elbows outstretched. In the UK we still don't really penalise that but in the Champions League they can send you off for that."
Bruce, though, did not see anything malicious in the challenge and described the collision as a hazard of the job.
"Nobody ever wants to see somebody cut but he's just jumped and he's caught him," said the Black Cats boss.
"It's impossible to jump without your arms out. It's why I've got a face like I've got. If you're going to play this game then sometimes, when you jump for the ball, you're going to get caught."
Sunderland dominated the first half and could have been ahead by more than just Bent's penalty, scored in the 24th minute after the impressive Fraizer Campbell was felled by Carr - although replays showed the foul was outside the box.
Birmingham improved after the break but the game looked to be over when Carr misdirected his header from Jordan Henderson's deep cross over keeper Ben Foster.
The introduction of 6ft 8in Serbian Nikola Zigic for his Birmingham debut gave the visitors more threat but it was Sebastian Larsson's delivery from set-pieces that really proved the difference as he picked out first Dann and then Ridgewell for the equaliser two minutes from time.
Bruce was disappointed by the manner of the goals but took encouragement from Sunderland's performance.
He said: "It's a disappointment. The one thing we spoke about all week was defending set-pieces. Larsson's delivery we know is excellent and so it proved.
"With being 10 men, the longer the game went, the deeper we got unfortunately. Sometimes it's not your day and it wasn't today, but there were a lot of positives to take from it."
McLeish, meanwhile, admitted his side had been poor, saying: "There's 37 games to go and I would hate to go through every game watching that. It was a tough game for us. We didn't pass it the way we can.
"I felt we were lacking a little bit of sharpness in one or two areas. We caved in, and it was self-inflicted, although it wasn't a penalty because it was outside the box.
"But we showed in the end the fantastic resilience and spirit that the players have got. When you've got set-piece accuracy from somebody like Larsson, it just needs somebody to be on the end of it."