The Sun says it was the fourth sending-off of Crouch's career but he could be in more trouble.
Chelsea boss Avram Grant condemned the challenge.
He said: "Crouch didn't need to do it. It was by the touchline in the middle of the pitch.
"Rafa (Benitez) was angry about something that happened before. I respect him a lot. Maybe he was angry at the other tackles.
"But the number of fouls Liverpool made on Mikel John Obi today. I think there were seven or eight in the first half.
"The priority of the referee should be to protect the game. You see what can happen to players. JT is out for six weeks.
"I didn't see those kicks. But, even so, Peter Crouch shouldn't have done that.
"I like players to play aggressively but not illegally. The tackle on JT and today - it didn't look good."