Kane had the chance to give Spurs the lead with a penalty won after the England international went down under a challenge from Reds goalkeeper Loris Karius.
The 24-year-old missed the spot kick, but did level with a second attempt from 12 yards after Mohamed Salah's strike had restored Liverpool's advantage.
Dutch centre-back Van Dijk has said that Kane went down easily for the first penalty, adding that there is a lack of discussion about the challenge.
"I think it is a dive," Van Dijk told reporters after the match. "You see [Kane] diving clearly and no-one is talking about it but I think it is a dive. There is a lot of discussion about whether it is offside, yes or no, but I think it was offside as well.
"You could just see him making that dive. The referee made his decision together with the linesman. It was good for us that it got saved."
Liverpool's next game is against Southampton on Sunday, while Spurs face Newport County in an FA Cup replay on Wednesday.