The Reds dominated the first half, but only led 1-0 thanks to Luis Diaz’s acrobatic effort.
United responded with two goals from Bruno Fernandes and Kobbie Mainoo, before Mohamed Salah’s late penalty saved a point for Liverpool.
After scoring 25 points and squandering numerous golden opportunities, Van Dijk was far more defeated than his manager at halftime.
‘It feels like a loss, and it’s our fault again,’ he told the BBC.
Virgil van Dijk cut a dejected figure as Liverpool conceded costly ground in the title race
Jarell Quansah made an error while Liverpool were leading to allow Man United a goal for 1-1
‘Unfortunately, an individual error occurred with the equalizer, and we had plenty of time to correct it, but we were in a hurry.
‘Despite being 2-1 down, we created so much.’
Before his centre back partner Jarell Quansah misplaced his pass, allowing Fernandes to equalise, Van Dijk and his teammates know they should have punished United at the other end.
Regarding the number of missed chances in the first half, the Dutchman stated: ‘We should have been 2-0 up at least, but in football, if these things don’t happen, you give them the impression they can come back, which they did.’
When asked if his mistake had any long-term consequences for Quansah, Van Dijk declined to comment.
‘He should not feel guilty,’ he added.
‘Mistakes happen in football. Everyone who has a career in football makes mistakes, and you can only learn from them.
Bruno Fernandes (right) pounced on Quansah’s error after he gave away the ball 50 yards out
Van Dijk (right) told his teammate to shake it off, saying mistakes are part of the game for players.
Following Liverpool’s draw, Arsenal now lead the table, with Jurgen Klopp’s side in second and Manchester City in third.
Nonetheless, Klopp was eager to preach calm at the final whistle, insisting that the title race is far from over despite a draw against their bitter rivals.
‘We were in a bit of a rush – I’d have loved us to take an extra touch,’ Klopp told Sky Sports about the number of missed chances in the first half.
‘You always have to take something different from the game.
Kobbie Mainoo fired United ahead to flip the game on its head after Liverpool had dominated
It took a late penalty from Mohamed Salah to rescue a point, and Liverpool is now second.
‘I know the outside world will be nervous, but we must remain calm; it will be full of life, excitement, and desire.
‘The goals we’ve scored have gotten us here. We need to build on that. We will deal with it properly.
‘I’m not thrilled, but it’s fine. You accept what you get. “If we had been more clinical, we could have won here.”