Phillips has had few opportunities this season, and McLeish admitted he received enquiries from Premier League and Championship clubs during the January transfer window.
But he has promised the 36-year-old he will have a greater involvement during the second half of the campaign, and believes he is still capable of making an impact.
McLeish said: "Kevin will never lose that ability he has got in the box.
"He might lose his teeth, he might go bald, and his legs will go at some stage, but he will always have that magnificent technique and touch of a top player.
"The morale of any player can be affected when they have been a first-choice player all their career and then find they are not playing every week.
"It has been difficult for me to keep walking by him in the corridor every day saying 'Keep your chin up'.
"But Kevin has been an exemplary professional. I spoke to him after the transfer window closed, during which time we had had enquiries from all sorts of clubs.
"I didn't really want him to go, and I've told him he would have more game time during the second half of the season.
"He was delighted to hear that, and we saw a spring in his step in training. He ghosts into areas where the ball might drop, and that is the mark of a genius."
McLeish admitted Phillips probably deserves a starting place, but is still to make his mind up about his line-up at West Ham in midweek.
He said: "I still feel he's going to be a big impact player for us, but after today he probably deserves a start.
"I've got to consider the right tactics for the team but, if you get the ball into the box, Kevin will score.
"He looks bright and sharp enough to continue playing after this season, but he will make the decision on things like that."
Phillips has had a phenomenal scoring record against Wolves wherever he has played, including a hat-trick for Southampton in 2003 and four goals in two games for West Brom during the 2006-2007 season.
McLeish said: "I knew his scoring record was very good against Wolves. I knew it was a weapon that had done damage to them in the past, and it has happened again, I am glad to say."
Wolves boss Mick McCarthy admitted this reversal was a hammer blow given how well his players performed for the majority of the match.
He said: "I have not been in our dressing room before and seen the lads as disappointed as that after a game.
"You feel hard done by, and it is hard, but we've got a game on Wednesday (against Tottenham), and that is the motivation we need.
"If we play like that in our remaining games, I don't think we can be written off.
"I had no doubt that the team would perform today, and they have done that on many occasions this season."
McCarthy added: "Birmingham started the game very well and we had to weather the storm, but after that we played very well.
"After half-time we were on top, and when that is the case, you need to take your chances. We didn't, that has cost us, we invited a bit of pressure which didn't help, and have paid the price."