Lambert was incensed by the spot-kick awarded against Villa striker Andreas Weimann for handball during last weekend's clash at the Etihad Stadium.
Lambert admitted a Football Association charge of improper conduct and, in addition to the ban, has also been fined £8,000.
He said: "I've admitted the charge. I still stick by the decision, that it was a shocking decision. It annoyed me at the time, but you can't change it.
"But if you're only about 40 yards away, how can you not see it. Nobody claimed for it.
"It might not have changed the result or whatever but it certainly changed the pattern of the game because we were well in it.
"The aftermath happens and then you end up getting done for it."
Lambert also confirmed striker Darren Bent was fit after missing three matches with an ankle problem.
The Villa boss insists his relationship with the England international is "fine".
Bent had lost his place in the starting line-up to Christian Benteke before suffering the ankle setback.
Lambert said: "Darren trained this week and is back which is pleasing.
"The players against Manchester City and Manchester United couldn't give any more. There wasn't too much wrong with that side but I have got options there if I want.
"Darren has been fine around the place and there has never been a problem anyway."