The Serbia international, a summer signing from Valencia for a fee believed to be in the region of £6million, finally opened his Blues account in last night's 3-1 Carling Cup third-round triumph over MK Dons at St Andrew's.
Zigic, who stands at 6ft 8in, brought down a neat looped pass from Jean Beausejour before coolly flicking the ball past keeper David Martin while under pressure from Dons defenders.
McLeish admits the towering frontman is still adapting to life in England and the demands of the Barclays Premier League, where he is finding more long balls than usual coming his way.
But the Scot hopes by opening his account - and getting more crucial match fitness under his belt - he will gain the necessary belief to push on and show why he was seen as an important addition to Birmingham's ranks.
"Let's hope that goal will be big for him," said McLeish.
"He's still adjusting to the pace of the game, he has admitted that it's quite quick and even the aerial stuff is new to him as such.
"You wouldn't believe that, I know the big man is 6ft 8in, but he would normally do two or three aerial jousts in the games in Europe and quite often he's been on the end of those jousts to score vital goals for Racing Santander, Valencia and Serbia.
"So he's been taken a little bit by surprise by how many times it comes up to him in the air, so that's a little bit different and he's having to adjust to that.
"But I hope that (goal) will do him good.
"He could have had a hat-trick to be honest, he maybe should have pulled the trigger in the first half and the position he got into at the back post (in the second half), we would like to see him get into those positions more."
McLeish is today waiting for news of how long he can expect to be without James McFadden.
The Scotland international underwent surgery last night to repair the knee ligament injury he sustained in training last Friday and should now find out the length of his rehabilitation.
McLeish will at least be pleased with the replacements at his disposal with fellow midfielders Alexander Hleb and Craig Gardner scoring either side of Zigic to hand Blues a quickfire 3-0 lead in a devastating four-minute spell.
Their npower League One opponents refused to lie down, though, and got their just rewards 10 minutes from time through Aaron Wilbraham's consolation.
Dons did the Football League proud with their passing approach and never-say-die spirit, and manager Karl Robinson believes if they can show the same qualities in their battle for promotion then they will not go far wrong.
"The players gave themselves and the football club credit - the passion we showed, the enjoyment and love for the game shone," he said.
"If you keep doing what you're doing and keep playing football then you won't go far wrong.
"I'm just happy, when we conceded three goals a lot of teams would have crumbled - and I don't think that was the case with us.
"We kept moving the ball and kept doing the right things.
"I want to stress that if our players keep doing that at our level then we can cause an awful lot of damage. It's important to keep believing that we're doing the right things."