West Brom boss Allardyce told BBC Sport: "I can praise the players on the pitch for staying in the game, keeping their shape and trying to get one back. We slipped up with a couple of goals. The performance was not very good but at least the 10 men battled away. I'm very disappointed in the sending-off and the first goal.
"Jake Livermore, I have no problems with that [red card] but why did they not look at the Kortney Hause one on Grady Diangana? At least Martin Atkinson should be asked to look at it by VAR. That is wrong. I don't want to talk about VAR, I have enough problems with my own team.
"An easy one next [Liverpool]. We will give it our best shot, no-one expected us to battle against Manchester City and I did not see that tonight, we need to find that."
Aston Villa head coach Dean Smith: "To win three games away from home 3-0 shows we are in a good place. We started really well and our energy levels were there to see - we controlled it from start to finish.
"There were times last season when the opposition went down to 10 men and we tried to force it but we were patient.
"We missed a number of chances to make it 2-0 and the offside call for Ollie Watkins was very marginal. I don't think they had a shot on goal against us all game."