The Argentine shot stopper got the better of Kane and his teammates in a 1-0 win over Villa over Bayern in the Champions League.
While Kane was disappointed with the result on Wednesday, he did acknowledge Martinez’s classy display.
He stated: “We could probably have played for another half-an-hour and not scored.”
Kane added: “From our point of view, it was one of those nights. Their keeper had one of those games, where it keeps coming off him. Even my chance at the end, he pulls off a fantastic save so you have games like that.
“The important thing for us is not to panic. We have had a really good start to the season. We are playing a really good style of football.
“As the coach would say, there are areas where we need to improve and we know that.
“Villa are a good side. There is still a long way to go in this competition to really see how it pans out.”