McLeish thought it was a well merited victory carved out by goals from Liam Ridgewell and James McFadden, although they had to survive a late challenge following an own goal from Scott Dann.
"I thought we deserved to win. I thought the players gave everything, in terms of attacking play," the Blues boss told Sky Sports after the match.
"We were very positive. There was great play from McFadden joining in with the front two and Seb Larsson worked liked a Trojan.
"At the end we got a little bit nervy after we gifted them a goal, but I felt overall we really deserved it.
"Two seasons ago we might have dropped points in that game but today the resilience of the squad and the new kids that are in the team, I think they made a difference."