Rodri headed in the winner to cancel out John McGinn’s opener after 20 seconds.
“Cashy was harshly done for the first yellow card but it was a stupid decision from him for a second yellow which was well deserved,” said boss Dean Smith with Villa 11th.
“He’ll be down and will be down after the earful he got off me in the dressing room afterwards. We won’t have many better chances of beating a team as good as Manchester City.
“We had a great start to the game, we talked about playing balls in behind their full-backs. Then, to be fair, I was stood there watching some wonderful passing and moving from Manchester City.
“But the two goals are what disappointed me the most, if Manchester City are cutting us open with one or two-touch passing and scoring excellent goals it’s a little bit easier to stomach.”