Referee Michael Oliver lost control of the final Merseyside derby at Goodison Park, Liverpool captain Virgil van Dijk said, after the visitors were held 2-2 thanks to Everton skipper James Tarkowski's last-gasp equaliser.
Everton's Beto opened the scoring in the 11th minute before Mohamed Salah set up Alexis Mac Allister's equaliser and then scored his own in the 73rd, putting the league leaders on course for victory.
But Tarkowski's 98th-minute strike shattered their hopes.
Abdoulaye Doucoure celebrated Tarkowski's goal in front of the away end, sparking a heated reaction from Liverpool native Curtis Jones, which led to a post-match melee.
Consequently, Doucoure, Jones, Liverpool boss Arne Slot, and assistant Sipke Hulshoff were all shown red cards.
"We saw how they celebrated the goal, they have all the right to, but I think Doucoure at the end wanted to provoke our fans and Curtis didn't think it was the right thing to do," Van Dijk told TNT Sports.
"You know what happens when there is a tussle, I think the referee didn't have the game under control and I said it to him. It is a fact, both teams had to deal with it. We take a point and move on."
Van Dijk said the draw felt a bit like a loss, having conceded the equalizer in the dying moments.
"Because it was over extra time and I think the referee had a big part in the game in terms of certain challenges were given as a foul and similar were not," he added.
"We all know this is their cup final and they will do everything in their power to try and win against us. This year, you see them scoring at the end and it's obviously a big boost for them but it's a blow for us."
Liverpool have picked up 57 points from 24 games, seven ahead of second-placed Arsenal. They host Wolverhampton Wanderers on Sunday, while Everton, in 15th place, visit Crystal Palace on Saturday.