Liverpool edged an entertaining encounter at Anfield 4-3 and Klopp celebrated Diogo Jota's last minute winner in front of fourth official John Brooks.
Klopp received a yellow card from referee Paul Tierney for his antics.
The German manager then insinuated in his post-match press conference that Tierney had an agenda against Liverpool.
Back in October, Klopp was handed a one-match ban, fined £30,000 and warned of his future conduct after berating an assistant referee when Liverpool played Manchester City.
Sutton believes it is about time Klopp was severely punished to deter others from following suit.
Sutton told BBC Sport: "For the way he acted on the touchline, he should be banned from the technical area.
"I don't think a fine is enough. He's got previous.
"It's a big deal. There will have been coaches and kids watching and thinking it's OK to run towards and abuse officials.
"As far as I'm concerned, Klopp should be banned. He knows what he did was wrong."
