The Italian was given a straight red card by referee Andre Marriner for a stamp on Meyler's shin at the end of the first half, just two minutes after team-mate Lee Cattermole was dismissed for a late tackle on Ahmed Elmohamady.
Carlos Cuellar's own goal had already put the hosts ahead and they claimed all three points against their nine-man visitors, but former Sunderland boss Bruce was angered by Dossena's foul.
He told Sky Sports: "I've known lee for a long time as everybody knows. I've signed him twice, but the big thing with that challenge in my day probably would only be a yellow card.
"The directive now is that if you leave the floor with your studs showing, even if you don't touch the player, then it's a straight red card.
"The other one (Dossena's tackle) should be three red cards. They're ones that hurt professional footballers; over the top and a stamp on his ankle. Meyler is lucky he has got away (without an injury).
"For someone who has had horrific injuries, I am pleased he has got away with it. It was an awful tackle that no one wants to see."
Bruce was also disappointed that his side were not able to build on the opening goal.
"I'm trying to recall If I've ever played against nine men for so long and I don't think I have," he added. "The longer it went on the more frustrated we got.
"To be fair to Sunderland they stuck rigidly to their shape, packed the penalty area and the more crosses we put in there the more bodies there were.
"We needed the second one to calm everybody down, but we'll take it. It was a big win which takes us 10 points ahead of Sunderland and Crystal Palace with a quarter of the season gone. That's a very nice return for us."
