Substitute Phillips was adjudged by referee Kevin Friend to have been brought down by Patrick Vieira for the spot-kick which Craig Gardner converted to earn Blues a 2-2 home draw.
Mancini insisted the 37-year-old striker "had dived".
"It isn't a penalty. It is nothing. It is impossible for that to be a penalty. If that was a penalty then there would be five penalties in every game," said Mancini.
But McLeish gave short shrift to the claims of his counterpart that the penalty should not have been awarded.
He said: "He (Mancini) would say that. If you look at the penalties given against us this season, they were much, much softer than that.
"I'm sure City have had their fair share that Roberto would claim were penalties and were probably of the dubious kind.
"For me that is a penalty because Kevin turned Vieira, has flicked the ball past him, and Vieira has clattered into him. How is not that a foul? Kevin never dived. Kevin is not a diver. He is a real true English gent."
On the performance, the Blues boss said, "It was a great performance second half.
"We were a bit sloppy with the goals we lost. You can't afford to give free-kicks away on the edge of the box against quality set-piece players such as Kolarov.
"But to fight back the way we did second half, we really made it tough for City. There's no doubt we made it a really hard night for them."
Source: PA