Kanevskyi participated in the 1962 FIFA World Cup in Chile, about which he stated that it was of lower level in comparison to the UEFA Euro 1996 in England. Among the brightest highlights Kanevskyi mentioned about his meeting with Pelé, receiving a good monetary bonus and traveling back to Moscow by way of Paris. He also said that was able to receive an autograph from Pelé, while sitting next to him at the Brazil – Czechoslovakia final game. After the championship, Konstantin Beskov was placed in charge of the Soviet Union national football team and Kanevskyi was removed from the team.