The 21-year-old was an unused substitute as Arne Slot’s side extended their lead at the top of the Premier League.
Despite being a key figure under Jurgen Klopp last season, Elliott has struggled for regular minutes since Slot’s arrival.
“The trouble is for players like Harvey Elliott, I watched him and I was really impressed with what I saw,” Tim Sherwood said on Sky Sports’ Gillette Soccer Special.
“The other boys are coming onto the pitch.
“He’s made five subs there tonight, and still no Harvey Elliott and you know, he’s not happy. He sat there and his face was so angry and annoyed.
“I quite admire that. You know, that boy is not going to sit there and just not play.
“He will want to leave that football club, I know it’s a brilliant club if he can fight his way into the team, but if he’s not going to play on a regular basis.
“They’ve got players like that and you need players like that, who want to play and want to affect it. At the moment, a top-quality player like him is sitting there and he’s getting no game time.
“If you don’t play and listen, he would be happy picking up a trophy and a medal but in the end, he will want to contribute a lot more than what he’s done.”