Zigic put Blues ahead after 33 minutes but Samir Nasri levelled from the spot just before half-time, with Marouane Chamakh slotting home a well-taken second goal two minutes after the restart which proved enough for all three points.
Wilshere then showed his immaturity with a reckless challenge on Zigic in the closing stages which earned him a straight red card and a three-match ban.
"It was a bad tackle and if he does not get a red card for that, then we pack our bags and go home," McLeish said.
"Zigic was lucky not to get a very badly damaged leg. We have had to put up with the Eduardo stuff for the last couple of years, and it is scandalous. It was a mistimed tackle from Martin Taylor and caused terrible damage to Eduardo - but that tackle could have caused Zigic a lot of damage.
"We know Jack Wilshere is not a dirty player, but it does show you players can mistime in this hurly-burly game in football. Everybody has to recognise that. It was a bad tackle and it was the correct decision."