Villa have now scored only one goal in their last three games and their lack of goals was emphasised in this latest performance as 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% 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.
“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.
“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.
“When it was 10 again 10 it was a better game but we created enough chances to have won.
“Since I walked through the door we have relied too much on Jonathan Kodjia and it was good to see him back in action for the first time this season.
“At times like this you have stay strong and fight the flak. There is no need for the hysteria. We have made a bad start in regard to the points but I know for a fact that we will climb the table.
“We need something to turn our way. We have to stay positive and one day we will take the chances created.”
Middlesbrough manager Garry Monk was delighted with the performance of his side which recorded their fifth clean sheet of the season.
Monk said: “Playing against an experienced and a good team we were under no illusions.
“I thought we started the game exceptionally well on the front foot. But you have to face adversity. We did that after Traore was sent off so early in the match and that was the most pleasing aspect of the game for me.
“It was more than a point. It was good to see the true character and the true mentality of the group.
“There are a lot of new players in a squad gelling together. Knowing this will stand them in good stead going forward.
“We have to build from clean sheets and if we put together a strong defence ethic we will able to win games and be in a good position.”