The Dutchman handed the Reds a two-goal lead in the first half of Saturday’s Premier League meeting at Anfield after twice heading in from Trent Alexander-Arnold deliveries.
It became an uncomfortable afternoon, however, as Alisson Becker was sent off 15 minutes from time and Lewis Dunk scored from the subsequent free-kick.
But Van Dijk and co dug in to preserve the slender 2-1 advantage, stretching their lead at the top to 11 points, and the centre-back felt it was a commendable result.
“Obviously we’re disappointed with the way we ended the game,” he told Liverpoolfc.com.
“We conceded a bit of a strange free-kick, the red card for Alisson, and we should have done better. But it’s not easy to play every couple of days and make sure we are more than 100 per cent.
“But we try to do that. The beginning of the first half was good, towards the end of the first half I think we should have done better. But it’s something we have to look at and try to improve.
“They are a very good side, you have to give them credit. They played well, brave and tried to get out of our press and at times it worked. So you have to give them credit. But we wanted the three points and got them.
“We have to show character, we have to fight. It was not an easy game, especially at the end. We had to dig deep and we did.”
Since the start of last season, no defender in the Premier League can better Van Dijk’s tally of seven goals – yet the No.4 still believes he should make more frequent attacking contributions.
“I try to be important,” he said. “With my height and my ability to be dangerous in the box, I could be even more effective.
“But it’s not easy to always be marked by the best defensive header of the opponent. But today I was able to sneak away twice.”
Liverpool now hold an 11-point advantage at the Premier League summit, with third-placed Leicester City set to host Everton on Sunday.
The latter will then visit Anfield next Wednesday night as the packed fixture list continues, with Van Dijk conscious of the need for a quick recovery before the Merseyside derby.
“I’m looking forward to every game and obviously Wednesday is going to be a good one. Everyone is looking forward to that,” added the Netherlands international.
“What we have to do now is make sure we’re more than 100 per cent on Wednesday. Luckily, we have some time to recover and make sure we’re ready.”