It completed a miserable day for Hodgson's side, who have lost five of their six games since the Premier League resumed.
"Christian Benteke has missed a lot of football this season through injury and got himself fit to play," said Hodgson.
"Now he has taken himself out of the last three of them for kicking out at an opponent. There is nothing I can say to excuse it. I'm obviously very unhappy about him being sent off.
"Quite frankly I don't know what he is going to be able to say to any of us to justify it other than the fact the red mist came down. He did something he is now going to regret."
Trezeguet scored twice as struggling Villa secured a first league win since 21 January to move to within four points of safety with three games to go.
"We have found it hard this season and there is no getting away from that," said Smith after his side's first win in 11 league games.
"I know these players can play under pressure. We have been playing tournament football since we came back.
"We haven't got the points we need but we're still in the tournament."
In an eventful game at Villa Park, Mamadou Sakho thought he had put Palace ahead when the ball appeared to strike the defender's shoulder on its way into the net - but it was ruled out for handball after a lengthy delay, much to the visitors' dismay.