Villa have now scored only one goal in their last three games and they failed to take advantage of playing 10-man Middlesbrough for an hour.
Former Villa winger Adama Traore was sent off after just four minutes but Villa could not take advantage before losing Henri Lansbury to a red card midway through the second half.
Bruce said: "We had 73 per cent possession and 19 attempts on target and you cannot believe that you can miss them at this level.
"It is endless and it is a huge frustration in a big game especially when the referee did his best to level things up with the sending off of Lansbury."
And the former Hull City chief felt the decision to send off his man was incorrect, while Traore had to walk.
"I thought the decision on Lansbury was a yellow card as we had three players behind the ball and in my opinion I didn't think it was a red card,” he added.
"I don't like seeing a player sent off but Middlesbrough's Adama Traore left the floor and it was reckless, dangerous and awful. But he deserved the red card."