Blues dominated their West Country visitors from start to finish and could easily have extended their goal tally.
But it took almost an hour for Blues to break City down, courtesy of Chris Burke's opener and Clark admitted he was fearful that his side wouldn't find the net.
"After about 50 or 55 minutes I thought it was going to be one of those nights where we were totally dominant and had lots of chances and it wasn’t going to happen for us," he said. "But we kept plugging away and we got what we deserved.
"We got at them from start to finish. My wide men probably had more chances at goal tonight and more shots than in all the games combined beforehand at home and that’s because we were positive.
“We played off the threat of our strikers who were very dominant, and we took gambles and risks which we are allowed to do. I want my team to do that at home. It’s the only way you’re going to be progressive. I thought we played some excellent stuff at times and I’m just a little bit disappointed that we didn’t win by four or five to give the crowd a real show in terms of goalscoring, but I think the performance deserved it."
Clark feels that a lot of the success his side achieved against City was down do doing the basics correctly.
"I’ve just said to the players that they’re a very, very talented group and there are not many better," he added. "It’s about doing the basics right and having a talented group of players who are probably better than most other teams in the league. When you do the basics right nine times out of ten you win football matches.
"Someone asked me before the game if Barnsley was still a hangover, but I said it wasn’t because it wasn’t a hangover for the last 20 minutes against Huddersfield or the second half against Ipswich when we missed three absolute sitters to win the game 3-1. So I was never of that thought process that it was affecting the players. I just felt we needed to perform from the first whistle like we had from the 46 on Saturday. If we’d done that on Saturday it would have been a positive result for us but we’ve done it tonight.
"What we’ve got to do is put back-to-back runs together and go on a run of winning football matches. We cannot have the up and down scenario. We’ve now got a tough game on Saturday but we’re relishing it."