Premier League referee Jon Moss ruled Kane had been brought down after an apparent slight touch from goalkeeper Loris Karius, after being controversially allowed to play on despite being in an offside position.
Kane missed the ensuing penalty, however redeemed himself from the spot in added time after Van Dijk was adjudged to have fouled substitute Erik Lamela.
However, £75m club-record signing Van Dijk believes Kane was lucky to get the first penalty, especially after Dele Alli had been booked for diving in the box minutes earlier - his third such incident since his debut in 2015.
"I think it is a dive. You see him [Kane] diving clearly and no one is talking about it but I think it is a dive," said Van Dijk.
"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.
"[Whether Kane should be banned] is not something for me. I thought it was a dive that is my opinion and the referee thought it was no offside and no dive and he gave a pen. Good for us that we saved it."
Van Dijk however was also clearly unhappy with the award of the second penalty when Lamela went down after the Dutchman tried to clear the ball and was judged to have swiped the Argentine's leg.
"I saw him coming in the end and I try and hold my leg in, he just pulled his body in front of the ball and he goes down," he said.
"The ref said play on and I was very disappointed that the linesman said otherwise.
"I don't think that is a penalty, same with the first one. That is also clearly not a penalty.''
Van Dijk was keen to recognise Mohamed Salah's brilliant second goal of the match - a twisting, turning effort past three defenders and Hugo Lloris.
"It was a good game for the fans to watch. For us obviously we are disappointed that we didn't get the win in the end," Van Dijk said.
"There were loads of things going on. I think the most annoying feeling at the moment is we should have won and kept the 1-0.
"It was a good goal from Victor and unlucky that we didn't win.
"It [Salah's] was a fantastic goal and to get a penalty [given against] in the last second of the game was not good.
"Everybody should talk about Mo's goal any way. Everyone can see how good he is and he showed that today as well."