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Liverpool defender Van Dijk hobbled off with a knee injury in the 11th minute after being challenged by Jordan Pickford, but the Dutchman left his mark on the game.
Rodriguez has been in fine form since arriving at Everton and Ancelotti admitted he would play no part against Southampton this weekend - thanks to van Dijk.
"Unfortunately, James had a problem during the game," Ancelotti said per Paul Joyce.
"He had a mistimed tackle with Virgil van Dijk at the beginning of the game and I think he will not be available for the game against Southampton."
Ancelotti also defended Pickford for his challenge on van Dijk, admitting the England international is 'very sad' about the situation.
"To be clear, we are really sorry for the injury of Virgil van Dijk," the Italian added.
"Every one of us hopes he can recover soon and well.
"There was this contact with Jordan Pickford: it was mistimed contact. But the fact the Premier League is so fast, it is not so difficult to arrive a little bit later.
"Jordan arrived a little bit later but his intention was to try to reach the ball. It was not to hurt Virgil van Dijk.
"To say it was premeditated, and this and that, in my opinion, is too much.
"Virgil van Dijk knows this. Jordan is really sad, really disappointed [that he is injured.]
"It was a strong contact, maybe mistimed, but sometimes in football it can happen."
Reds midfielder Georgino Wijnaldum commented on the challenge prior to Liverpool's Champions League clash with Ajax and he admitted the squad are 'devastated' about the injury to van Dijk.
"This was different than normal," Wijnaldum said via The Mirror. "The way it happened was really hard for us, and everyone still has a really bad feeling about it.
"None of the players slept. It's a hard one to take and it was a hard one for the team.
"Virgil is a really important player in our team - he has showed that since he came in. He is a leader. It's up to us to show that we can still put in good performances without Virgil. We have to."
Featured Image Credit: BT Sport
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