Speaking to Sky Sports in the immediate aftermath of the game, the Dutchman shared his view that there was only one team trying to win.
That opened him up to criticism from former United captain Keane, who said: “We heard Van Dijk speaking there, a lot of arrogance coming out of them, dissing United like that.”
But, when asked about those comments, Van Dijk doubled down on his view that the visitors set out simply to avoid another 7-0 drubbing at Anfield.
He said: “I like Roy Keane, if he said that then it’s fine. He is Man United throughout and I understand he could react like that, but I felt what I said and there is absolutely no arrogance in that.
“Everyone who watched the game probably felt the same. We move on. We had the opportunity and we couldn’t score and that’s the frustrating part.
“Obviously they are not in the best situation, and if you come here after you have lost last here with a big number you are going to be more than happy with a point. Everyone could see that.
“You could see what their game plan was and what we tried to do and I felt what I said was right and we move on.”
Liverpool failed to find an opening goal on Sunday despite taking 34 shots from over two-thirds of the possession across the 90 minutes.
And Van Dijk wants his teammates to show more patience in future as they attempt to unlock a low block defence.
He continued: “If we learn from it I’d be fine with it. We’ve had many games already this season where we have played against low blocks and done well so we have to learn from it and keep going.
“I think we did everything to try to win the game. Maybe trying to force it a little bit at times and we could have made a better decision, but it was hard to break the low block down and unfortunately we didn’t win.
“You push, you push, you push and try to do everything in your power but today was one of those days we couldn’t find the right decision to score a goal. We move on and have to learn from a lot of moments – and we will – and focus on Wednesday.
“You do overlaps, you try to cross the ball and at times – I won’t say every time – we forced it too much and find a solution which wasn’t there but that’s football. It didn’t work out the way we wanted but we had opportunities and unfortunately couldn’t score.”
And the captain hopes the extra 7,000 fans that have been added to Anfield’s attendance this week can help get Jurgen Klopp‘s side over the line.
He added: “I love it. We need them. We need them even more Wednesday because it is three days after a demanding game and everyone is a little fatigued.
“We need that energy from the crowd to push us forward from the very first minute to the very last, and hopefully we can progress.
“We need everyone for that because today was demanding for everyone and I’m looking forward to being out there again, under the floodlights with the fans behind us. Let’s go for it.
“It’s the first trophy that could be in reach and it will be a very tough game as West Ham are also in a good moment with good players, so I will give everything to be ready for that like I always do.
“Let’s hope this year is a very good competition for us.”