Bruce ruled himself out of the running to take over at Newcastle on Wednesday, with current St James' Park boss Alan Pardew looking set to assume the reins at Crystal Palace.
But Bruce says he had the chance to take on the club he supported as a youngster when Robson left in 2004.
"I made a big error," said Bruce, who had been among the favourites to succeed Pardew this time around. "I had the opportunity to go when Sir Bobby Robson left and I stayed loyal to Birmingham.
"In hindsight, maybe I should have taken it then.
"But now it wouldn't be right for me to take part in any speculation.
"I hope it's quashed and it goes away, but I doubt it."
Asked whether he would one day like to manage Newcastle, Bruce responded: "I haven't even given that a thought."
While Bruce - out of contract at the end of the season - has been talked about as a potential successor to Pardew, he has also come under pressure in his current role, with Hull perilously poised above the relegation zone on goal difference alone.
Despite guiding the club to the Premier League and last season's FA Cup final, Bruce knows the importance of improving his side's current form.
"I don't think we can genuinely say that we're all safe," he added. "There was a statement from West Brom to say that Alan Irvine [who has since been sacked] was safe.
"We're all judged on results and, for me over the last two months, they haven't been good enough for that standard we've set.
"There are people who have been calling for me [to go] and forget what's happened in the last two and a half years.
"That's the way it is, it's a bit fickle, but I won't take anything for granted."
When asked whether he expected the loyalty he had shown the club to be replicated by chairman Assem Allam, Bruce added: "That's something you can ask him, but I can't take anything for granted."
