Clark had called for more determined attacking play in the aftermath of recent results and he was rewarded with this success - Birmingham's first at St Andrew's in five games.
The Midlanders carved out their belated success with a 59th minute strike from Chris Burke and a second goal from Marlon King after 73 minutes which plunged the struggling visitors to their sixth successive defeat.
Clark said: "After 50 minutes I was thinking it was going to be one those nights where we were totally dominant and creating lots of chances and it wasn't going to happen for us.
"We kept plugging and got what we deserved. If we had won four or five Bristol City could not have had any complaints.
"My wide men probably had more chances and shots on goal than they have had in all the previous games combined because we were positive and played off the threat of our strikers.
"We took risks which we are allowed to do playing at home. This is the only way we are going to be progressive.
"We played some excellent stuff at times and I am just a little disappointed we did not win by four or five goals to give the crowd a real boost."
Clark paid credit to Burke, saying: "His was a complete performance. He made numerous chances, scored a goal and also won us a penalty.
"He was in very good form and I hope that is the kick-start to his season because this would be a massive benefit for us."