Hleb, a deadline-day signing from Barcelona on a season-long loan, cut an impressive figure as he made his home debut for Blues in their 3-1 Carling Cup third-round triumph over MK Dons.
The Belarus international broke the deadlock with a sweet strike midway through the first half before seeing two quickfire goals from Nikola Zigic and Craig Gardner all but wrap up the tie.
Hleb is still getting crucial match practice under his belt and becoming orientated with his new surroundings and team-mates.
McLeish insists he has settled well having been used to training with the likes of Lionel Messi, Andres Iniesta and Xavi at the Nou Camp.
But while the Blues boss admits his side can hold their own when it comes to the passing game, he acknowledges they are no match for the European giants.
Asked whether he has to manage expectations when bringing in players of Hleb's calibre, the Scot replied: "I suppose we do.
"Alex will be used to ball-playing centre-halves and maybe the possession game, but we play the possession game fairly well.
"We stopped doing it at the weekend after we lost two gifts of goals against West Brom.
"But we realise on the training ground that we've got a lot of good players who can pass the ball.
"There are some things that he'll have to realise, and he will realise, and he does realise, that we're not Barcelona."
McLeish also believes it is only normal for a player of Hleb's quality to have to accept responsibility to step up to the plate having made such a switch.
"Any top player who plays in any game, that is the extra challenge to them," he added.
"They're seen as top players so if they don't perform they're the first ones the press pick on.
"He's fitted in well, there's no airs and graces about him, he's actually quite a character and the players have taken to him."
MK Dons put in a battling display at St Andrew's despite the crushing four-minute spell that settled the encounter.
The League One side played some good football and got their just rewards for plenty of endeavour when substitute Aaron Wilbraham grabbed an 80th-minute consolation.
And manager Karl Robinson felt the difference in predatory finishing was a the key factor when it came to the gulf in class.
"That's why they're in the Premier League," he said.
"We had a chance with Lewis Guy - very similar to Hleb's one - and two headers from Dean Lewington in probably a six, seven, eight-minute spell and we never took ours.
"I thought their finishing was phenomenal and they play in the Premier League because there's very few opportunities created at that level.
"And when they do come along, you've got to make sure you've got enough quality to take them."