Liverpool had competed strongly during the first half, but Gravenberch was sent off for a second bookable offence in the 62nd minute. Manchester City took advantage through Erling Haaland, Jérémy Doku and Rayan Cherki, scoring three times in the second half.
The Liverpool captain felt his side had shown the right intensity before the decisive incident, although he acknowledged there were opportunities to improve their attacking play.
“First half was good from us. We showed our intensity, could've done better on occasions where we got on the break. They weren't massive chances but we showed we wanted to win and we had intensity which is the bare minimum,” Van Dijk told Sky Sports.
However, he believed the dismissal and City's quick response proved decisive.
“Second half the red card changed the game, especially when you concede quickly afterwards. We end up with 10 men is the fact and we concede quickly after and it becomes a difficult game against them again.”
Haaland put City ahead in the 65th minute, only three minutes after Gravenberch had been dismissed. Doku then scored in the 68th minute, before Cherki added a third in the 78th.
The defeat ended Liverpool's unbeaten start to the league campaign, while City maintained their perfect record under manager Enzo Maresca.
Van Dijk also reflected on the atmosphere at Anfield, where supporters had made their feelings known during City's first match since the verdict in the Premier League's financial case.
“I think the atmosphere is always good here, I've been fortunate to play in a lot of big games here. For other players maybe it was different but for me I was ready to compete and I think we showed that especially in the first half,” he said.
The Liverpool captain was asked separately about the verdict against Manchester City, but declined to offer a substantive opinion while the matter remained unresolved.
“The only thing I can say, because it's ongoing, is that I have really enjoyed the rivalry,” he said.
“But that is on the pitch, what has happened off the pitch is a totally different story.”
Van Dijk stressed that he would wait for the process to reach its conclusion before commenting further, distinguishing the sporting rivalry from the allegations and proceedings away from the pitch.
“Because it's still ongoing, it's not a good idea for me to comment on this,” he said.
“When it's properly settled I will definitely share my comments on it but for now let's wait and see.”
For Liverpool, the immediate concern is recovering from a first league defeat of the season. For City, the result was a significant victory in a difficult atmosphere, secured through three clinical finishes after the contest's turning point.