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"It was a dream start, I thought we deserved it and the new lads did really well," said Neil Warnock.
"I have told the players they have to enjoy it, when that whistle goes and I see a team putting everything out there for me, you cannot want any more that.
"We still have work to do, we were underdogs tonight and there will be a few more games in the coming weeks when we will be underdogs."
Warnock also heaped praise on matchwinner Bamba, who just over a week ago was still a free agent after leaving Leeds.
"Sol thinks he is Franz Beckenbauer at times, I have seen him try to do all sorts of tricks and flicks," said Warnock.
"I told him he needed to play for me, with no frills, just head it and kick it. He is as good as anything in the league doing that."
Whittingham gave the hosts a 25th-minute lead from the spot after Craig Noone was fouled by Joe Bryan, although the Cardiff winger looked to be offside in the lead-up to the challenge.
Bamba then doubled the Bluebirds' advantage in the 67th minute as he found the net from close range when Rickie Lambert's header came back off the crossbar.
Tomlin hit back just two minutes later and Bristol City had their chances to level, with substitute Bobby Reid missing a great opportunity in the dying moments to leave manager Lee Johnson frustrated.
"We were poor in the first half. I'm not sure if we were a bit posey as it was in front of the Sky cameras or if we were a bit naive, I would like to think it was naive," he said.
"But for whatever reason we went off the game plan, we were trying to play out from the back a lot and we are not technically good enough to do that at the moment. So it gives me some things to think about.
"I thought for their first goal it was offside. Offside is offside and you work all week to make sure your line is good but for some reason the linesman didn't spot it.
"It was a game of passion and tackling and you expect that in a derby, but I was just disappointed with the quality and the fact we didn't go away with the three points."