The 1-0 victory took Blues back to the top of the Championship table courtesy of a stoppage-time goal from Garry O'Connor.
"In the first half we were exceptional," the Blues boss told Sky Sports News after the game at St Andrews.
"In the second half we ran out of steam a little bit because our strikers had worked very hard to get on the scoresheet.
"We'd said to the lads 'you've got to go to the very end because it only takes a second to score a goal' and they came up trumps at the end once again."
McLeish singled out goalscorer O'Coonor for special praise as beside's his winning goal he was arguably Blues' man-of-thematch and may easily have had a hat-trick having hit the post with two efforts in the first half.
"I was really pleased for Garry O'Connor," McLeish said.
"He has now played in three successive games and he is obviously playing better from playing regularly in the side.
"He produced a fine all-round performance and, with a bit of luck, could have had a hat-trick."