Hleb, a deadline-day signing from the Spanish champions on a season-long loan, impressed on his home debut for Blues in their 3-1 Carling Cup third-round triumph over MK Dons on Tuesday night.
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.
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."
He added: "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."
Source: PA
Source: PA