Blues played poorly in the first half and were lucky to have gone in at the break still level at 0-0.
Their performance improved slightly after the break and Lee Carsley's first league goal of the season on 62 minutes proved to be enough for Blues to leave Home Park with a somewhat fortuitous three points.
"I said to the players at full-time that if there was ever a game that was ground-out then that was it tonight," McLeish told Sky Sports News after the match.
"In the first half it was difficult to see that we could get something from the game.
"There was though a definate response after half time and after scoring we were able to see the game out and take all three points."