Nathan Jones identified a change in mentality as the key to Luton's thrilling second-half comeback from two goals down.
The manager felt that was even more influential than the contributions of his two halftime substitutes, James Collins and Harry Cornick, who both scored.
City looked set for their first victory at Ashton Gate since January when Nahki Wells fired them in front on 31 minutes and Adam Nagy doubled the lead with a 38th minute shot.
But when Collins pulled a goal back with a 49th-minute header from a near-post corner the tide began to turn against Nigel Pearson's men.
Elijah Adebayo equalised with a clever first-time finish and Cornick completed the comeback with a 74th-minute winner, slotted past Dan Bentley from 12 yards.
A delighted Jones said: "The substitutions worked well, but the biggest difference in the second half was our mentality.
"We can't spend big money, but we beat teams in the Championship by doing the basics better than them.
"The players forgot that in the first half. We reminded them of it at the break and they took the message on board.
"I'm delighted for Harry Cornick because it was his first League goal of the season, even though he has been a threat wherever we have played him.
"He and James Collins helped turn the game and in the end I thought we deserved all three points because we were the better team.
"Even in the first half, we created good chances. Credit City for their first goal, but the second was a gift from us.
"It wasn't a case of being angry at half time. I just reinforced what we do best."
Pearson's short-term contract with City expires next month, but he is hoping to be given the job on a more permanent basis.
He said: "I have had some positive talks with the owners and hopefully there will be some firm news for our fans soon.
"I want the job, but this game showed exactly where we are as a club and how much work there is to be done.
"Our young players are doing well, but some of the others seem to want the season to end as soon as possible.
"It concerns me that the youngsters could be damaged by being in a side performing so poorly.
"But we have so many players unavailable that I have to go with them.
"They are not getting the help from the senior professionals that they need.
"We can't even win a game from two goals up. That demonstrates a soft mentality, which has nothing to do with tactics or formations.
"The goals we gave away were very poor and there is a huge job ahead to get things right."