The centre-back was penalised for a stoppage-time foul on Erik Lamela that led to Harry Kane converting from 12 yards to snatch a 2-2 draw in their Premier League showdown at Anfield.
But, overall, Van Dijk was an impressive performer alongside Dejan Lovren in a game that hints there is still so much more to come from the 26-year-old.
Van Dijk looked an absolute class act in the first half as he organised and defended effortlessly at times, alongside providing a much-needed commanding presence in the box winning numerous strong headers.
He kept Kane largely out of the game and made a superb block on Son Heung-min, but the kick on Lamela that gifted Spurs a second penalty and a point in injury time was a costly error.
The former Celtic man spoke to media after the game and still feels the best is yet to come:
“I have been out for eight months – last January until September really – and I didn’t play at Premier League level,” said the Dutchman.
“It is not easy to come back and especially when I have made such a big step as now, with all the eyes on me and they look at every small detail. I am just focusing on the team and myself.
“The football we play, the pressing, the different options with players, it is totally different.
“So you need time to get used to everything but I am working on it every day together with the team. I am talking with the manager and everyone who can help me out," Van Dijk added.
"We will see the best from Van Dijk after the summer"
The Reds' record signing scored on his debut against Everton in the FA Cup but could not prevent Liverpool from suffering back-to-back defeats to Swansea and West Brom, and he was subsequently rested by Klopp for the 3-0 win over Huddersfield last Tuesday.
The German manager has urged Liverpool supporters to remain patient with Van Dijk who has been Klopp's main transfer target since last season and expects the Netherlands international to improve as the season progresses.
"I'm very happy with him but there will always be ups and downs," said Klopp to Sky Sports.
"We will see the best from Van Dijk after the summer. We don't have the time to wait until then, why should we?
"He can bring a lot of things in already and that is good. We have had a lot of talks, it is quite difficult, our defending is different to Southampton. He has to get used to it."
Klopp admitted Van Dijk was struggling for full fitness after arriving from Southampton.
"When Virgil came here he wasn't match fit, that is the truth," said Klopp.
"He had a long injury, then he played, then he was injured. Then the transfer was an open case and he didn't play for Southampton, so it wasn't a consistent season.
"I haven't known him long enough to say 'yes you can play all the games in this moment'. He expected it, he is still a new player."
Van Dijk was one of three players, along with Danny Ings and Nathaniel Clyne, to be added to Liverpool's Champions League squad and crucial fixtures in Europe could be the perfect test for Van Dijk to prove he was worth his price tag.