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After a first-leg win, Liverpool were beaten at Anfield with a decisive goal by Ousmane Dembele before the visitors' success on penalties.
Despite the subsequent misses by Darwin Nunez and Curtis Jones in the penalty shoot-out, it was Van Dijk's actions, or lack thereof, that drew Rooney's ire during his commentary on Amazon Prime Video.
He fumed: "This goal from Liverpool's perspective is wrong in so many ways."
He criticised Van Dijk for failing to engage and leaving a gap for Dembele: "They are trying to press the ball and Van Dijk gets lazy.
"If you keep your eye on Van Dijk, he's walking and leaves a massive gap to Dembele.
All he has to do is come across and cover Dembele because there is no other pass for Paris to get out and he doesn't.
"Dembele gets it and he's got a lot of space, gets the ball out wide and then Konate doesn't switch on and then he reacts.
Dembele makes a good run and gets a tap in."
After the match Van Dijk called for the team to move past the defeat and focus on the upcoming Carabao Cup final against Newcastle.
Now we get ready for the next challenge at the weekend which is a beautiful one.
"I think we were pretty good today as well, and you want to go as far as possible, but we knew when we drew PSG it was going to be very difficult.
We saw in Paris when we struggled but we won, and today we saw a very good Liverpool side but we're out of the competition.
"Today from the first second and then extra time, when fatigue kicks in for both sides, it becomes more open but especially regular time, we showed a very good game.
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