Cameron Jerome's goal five minutes into the second half of the game at The Britannia Stadium seperated the two sides and extended Blues run to 11 games without defeat.
"I thought they were brilliant today," McLeish told Sky Sports after the match.
"I thought we really played good football, the ability was very evident and of course we knew we had to match the big physical presence of Stoke, and it was hairy at times but we coped and in the end I felt we deserved to win.
"Its another very valuable three points towards the Premier League security.
"The players were awesome today, I'm really proud of them, they are fantastic.
"We have to get security and then we'll take anything else as a bonus.
"We have given ourselves a fantastic opportunity to do well in the league this season and it was another difficult away tie and we felt, possibly, these lads that some day would run out of steam or maybe Lady Luck would go against them and we'll lose a game.
"But today I could see the determination on their faces in the dressing room before we went out, they weren't going to go into the New Year resting on their laurels, or being complacent and saying 'well we've got a bit of leeway, we can afford a defeat'.
"You see the way they played, they were absolutely outstanding."