England captain Kane scored four times in the first half after Harry Maguire's opener and a Filippo Fabbri own goal.
Emile Smith Rowe, Tyrone Mings, Tammy Abraham and Bukayo Saka completed the rout after the interval as England finished top of Group I to ensure their place at the tournament in Qatar in 12 months' time.
It was England's record win in a competitive international and Kane was delighted with the stylish way Gareth Southgate's unbeaten side achieved their qualification target.
"We were fantastic. It came to the last game and we were expected to win but we've done a good job. Fantastic to go through," Kane told ITV.
"We still need to keep working. I feel like we have been improving year on year. We have to make the most of the time, every training session to fine-tune the little pieces."
Kane, who scored a hat-trick in Friday's 5-0 win against Albania, moved alongside Gary Lineker on 48 England goals.
The Tottenham striker is behind only Bobby Charlton (49) and Wayne Rooney (53) in England's all-time list.
His 16 goals in 2021 is a calendar year record for England and he is the first Three Lions player to score three or more in successive games since Tommy Taylor in 1957.
"Fantastic again. Every time I wear an England shirt I am proud and when I score goals it is one of the nicest feelings I can have in my career. Nice to be among those names," Kane said.
Standout matches today