Skrtel earned both yellow cards for his fouls on Kane. A stamp in the 57th minute of the game saw the Slovakian receive a second booking and subsequent marching orders from the game.
The sending-off proved to be crucial in the game as the Three Lions eventually won 1-0 thanks to an injury-time winner from Skrtel's ex-Reds colleague Adam Lallana.
"It was hard fought, there were a few challenges flying about and sometimes when you are up there you have just go to work hard for the team and try and get into good positions and I felt I did that," Kane said of the summer Fenerbahce signing.
"The ankle is okay now. I will have a check on it and see if it's fully okay, but there were a few challenges that I felt could have earned him a yellow card but it didn't come.
"It was just a matter of time. It was a silly thing for him to do because he was on a yellow. The referee has seen it and it deserved another yellow card."