Frustrated Wolves fans had hit out at Solbakken during a run of nine games without a win, but they stopped the rot in clinical fashion at Ashton Gate.
Wolves effectively put the result beyond doubt with a four-goal salvo before half-time, and their relieved manager said: "The fans are entitled to be critical during poor runs and I have no problem with that.
"We are a big club and expectations are high. If there wasn't a passionate reaction it would suggest no one cared. It is something we have to deal with.
"Maybe we got the bit of luck we have been missing, the first goal being an own goal, but after that we played well.
"We lost David Edwards with a hamstring injury to add to the ones we already have, but other than that I am very happy.
"I hope we can be a December team because we certainly weren't a November team. But we will not get carried away by one result."