McLeish had words of praise for Hleb - who played for nearly 80 minutes at the Hawthorns.
And he also admitted he was "gutted" for James McFadden, who missed the trip to West Brom after picking up an anterior cruciate ligament injury to his left knee in training on Friday.
"The irony in talking about Hleb doing well on his debut is that we were planning to play an unchanged side from the Liverpool game because James had looked back to his very best in that match.
"We are gutted for James because he was not only in fine form but was one of the fittest players at the club. His body mass index levels were great and after playing so well for the club last season he looked to be running into another period of fine form.
"I said to the lads before the game 'let's go and win this one for Faddy' and for a while it looked as though we were going to do exactly that. Maybe I should have told them again at half-time!"