Steve Bruce felt two key decisions from referee Tim Robinson cost Villa the win that would have eased the growing pressure on his job.
The visiting boss had to endure chants for his dismissal at the end of the game following cries of “you don’t know what you’re doing” when he substituted Tammy Abraham in the closing stages.
Of the fans’ reaction to a battling draw, Bruce said: “There is a certain element that think I can’t do the right thing about anything.
“I know with a club of our size there is expectation. However, it is not a given to come to Bristol City and beat them three- or four-nil.
“Do they really think I wanted to take Tammy off four minutes from the end? I maybe should have taken him off 15 minutes before because he had signalled that he had a calf problem.
“I will get on with the job as always and do the best I can. I know with the squad of players I have that we will be there or thereabouts when it counts.
“Tonight we had a goal wrongly disallowed when their goalkeeper barged into Tammy yet got a free-kick, and were denied a blatant penalty when one of their defenders fell on the ball and handled it.
“We have lost two out of 10 games and I don’t know what I am doing. Thankfully I have been in the game a long time.
“I know that for some I will never be the answer. But the players were excellent tonight and they are the ones I will always protect.”
Bruce wanted to see City’s goal again before deciding whether goalkeeper Orjan Nyland was culpable in allowing Josh Brownhill’s low 16th-minute shot from 20 yards to escape his grasp.
But the manager was pleased with a response that saw midfielder Birkir Bjarnason head an equaliser in first-half stoppage time from Conor Hourihane’s free-kick into the box.
Bruce was unhappy, however, with some of the treatment dished out to Jack Grealish and claimed he is being targeted by Championship opponents.
City head coach Lee Johnson left the post-match press conference to one of his assistants, Jamie McAllister, who heaped praise on the team’s resilience.
“We wanted a response to what was a poor performance at Wigan and got it from every player,” said McAllister.
“It was a poor free-kick to concede just before the break and Callum O’Dowda has held his hand up for that. But we should have defended it better.
“Other than that I thought we defended really well as a team, with Adam Webster and Nathan Baker superb in snuffing out the threat of some of the best forwards in the Championship.
“Our failing was in the final third of the pitch, with our final ball or cross. We wanted to test their keeper more because he looked shaky at times.”
McAllister was at a loss to explain the reaction of Villa supporters at the final whistle.
“I thought it was absolutely crazy because Steve Bruce is such a top manager,” he said.
“Villa will definitely be up there at the end of the season and, for me, they have to stick by him because he is a very good coach.”