Dean Smith attacked the “farcical and pathetic” decision to allow Manchester City's opener to stand as Pep Guardiola's side stretched their unbeaten run.
Rodri put Bernardo Silva through on goal to score in the 79th minute, but only after returning from an offside position to dispossess Tyrone Mings.
But because Mings had controlled the ball, it was deemed a new phase of play and Rodri was not offside, a decision which infuriated Aston Villa boss Smith and saw him red carded for his complaints.
Smith said: "It's farcical. Are we just going to leave players behind the line then?
“He was 10 yards offside and come back and tackled our player, it's a pathetic law and a pathetic decision.
"I said to the fourth official David Coote 'did you get juggling balls for Christmas?' I don't think any other manager would get sent off for that.”
City then won a penalty in the 90th minute, converted by Ilkay Gundogan to seal the win, after Matty Cash handled the ball in his own area.
"Matty Cash is a yard away for the handball, he can't jump without his arms up,” said Smith.
“He didn't even look at it, it flabbergasts me. It was a poor performance from the officials and that's cost us."
City match-winner Bernardo, whose goal was his first in the league this season, said: "I haven't checked it yet.
“Our player was offside, but when their defender touched it, he stops being offside, I think. But I haven't checked it.
“It was a very important win, a tough game for us. Its been a long time since I've scored, so I'm happy to score.
“There's still a long way to go, but we're very happy. We're doing very well, very solid at the back. We're happy with the last two games and our momentum."
