The Scots took a massive step closer to qualifying for next summer's finals with goals from Kenny Miller, Lee McCulloch and James McFadden at Hampden Park.
But the win came at a cost to McLeish, as McCulloch and substitute Garry O'Connor picked up bookings which will mean them missing Wednesday's match in Tbilisi.
With Paul Hartley and Gary Caldwell injured, the Scotland squad will be stretched to the limit.
Darren Fletcher, who has not played since he injured his knee in the 1-0 win over France in Paris last month, will return - but McLeish could be forced in to calling up extra players.
He said: "It was the best game we have played at Hampden since I've been here.
"It is a massive step towards qualifying - but I have mixed feelings because we have some walking wounded and we have suspensions.
"McCulloch and O'Connor are suspended. It is too early to say who is injured. Obviously (Scott) Brown limped off, and 24 hours might make a difference - but we may have to call some people in.
"There were about five or six with ice packs on - (Barry) Ferguson, (Gary) Naysmith, Miller was hobbling - and Stephen McManus got some stitches in a head wound.
"He was a little bit concussed - but he was a stalwart, along with Davie Weir.
"Alan Hutton had a calf injury during the week, so he will probably have ice on that as well.
"The good news is Sir Alex Ferguson has given us the green light to call Darren Fletcher in, so he is joining up on Sunday.
"He is fit and he trained the whole week at United. He was left out of a practice match and he will be fit enough to play for United next weekend."
McLeish was left struggling for superlatives after yet another impressive Group B result, before Scotland's two final qualifying matches - in Georgia and then Italy at Hampden in November.
The Scots have won six games in a row for the first time since 1949, and McLeish said: "There was skill; the finishing was phenomenal - and some of the defending was terrific as well.
"We have two cup finals left, and to get this far should be above anybody's wildest dreams.
"We used to try and prove people wrong - but we are now proving them right.
"The bookies had us favourites; the pressure was heaped upon us - and by God, they responded again."
McLeish had a special word of praise for Paris goal hero McFadden, whose second-half strike eased the nerves after Andriy Shevchenko had given Ukraine some hope when he reduced the two-goal deficit.
He said: "Everybody needs players who can make a difference to their team, as well as the organised guys and the workhorses.
"It's always nice to have an ace in the pack, and McFadden has proved that time and again in the national jersey.
"It was a great performance."
McFadden revealed a "chilled" approach had paid dividends.
"There is massive expectation but for some reason this week, even in training and sitting about the hotel, nobody even spoke about the game," he said.
"And I think that was a good thing because our minds weren't really on the game until kick-off. That was the most important thing for me, just chilling out and then playing the game when it comes and trying not to read the papers.
"That's why you are a professional, you need to deal with it and I thought we dealt with it superbly."