Mohamed Salah had scored one goal in five Premier League appearances prior to Saturday's game against West Ham
Salah had been dropped for the game and clashed with Klopp as he prepared to come on as a 79th-minute substitute.
The draw leaves Liverpool, who are out of the Europa League, five points behind Premier League leaders Arsenal.
Sutton felt the incident did not reflect well on the 31-year-old, who is the Reds' top scorer this season with 24 goals but has not been at his best in recent games.
"I didn’t like it but I think Mo Salah is the one who was out of order," Sutton said on BBC Radio 5 Live's Monday Night Club.
"He is no different to any of his Liverpool team-mates and the truth is his form hasn’t been good since he has come back from the injury.
"It is nothing against Salah and the brilliant player he has been at Liverpool. He has been phenomenal but I think there is a line and unfortunately for him he crossed it."
Klopp, who is leaving Liverpool at the end of the season, brought Salah to Anfield in June 2017 and he has consistently been one of his most influential players.
But Sutton believes Klopp was well within his rights to choose the first XI he felt gave Liverpool the best chance of securing victory.
“You can’t live on the past," added Sutton.
“It is the here and now and Klopp decided to leave him out. That is his prerogative. He is the manager and Salah is no different to the rest of his team-mates.”
Salah seemed frustrated at something Klopp said to him as he was about to be brought on, and seemed to want to prolong the altercation before team-mates Darwin Nunez and Joe Gomez shepherded him away.
Afterwards, Salah declined interview requests, saying: “There’s going to be a fire today if I speak.”
Former Everton midfielder Leon Osman also felt the incident did not reflect well on the Egypt forward.
“If you act like that you are showing disrespect to your team-mates as well as the manager by basically saying ‘I should definitely be playing before them’," Osman said.
“Yes he has been their best player but you are all part of the squad, you all rotate for the most part, you shake hands when you go off the field because you have the same goal to try and win football matches.
“It is a sad end to the run they have had and the relationship they have had.”
-- Courtesy of Borneo Bulletin