Liverpool now hopes that Manchester City and leaders Arsenal, who are three points ahead, will make mistakes in their next four games.
Their season is in danger of ending as they suffered their second defeat in three games at Goodison Park.
Van Dijk questioned, “Do they really want to win the league?”
Defender Jarrad Branthwaite and forward Dominic Calvert-Lewin each scored a goal in the first half to put the Toffees ahead in the league for the first time since October 2010.
After losing 1-0 at home to Crystal Palace ten days prior, it was yet another blow as they lost the chance to draw even with the Gunners.
Van Dijk was extremely critical of Sports, saying, “We have no chance to win the title if you play like this overall in the game and not win any challenges and give the referee an opportunity to give a free-kick away.”