The Tottenham man managed just 19 touches before being substituted in the 74th minute – the fewest he has ever had in an England game when playing more than 45 minutes.
The last time he had fewer touches for Spurs while playing for more than 45 minutes was against Manchester City in April 2018 (17 touches in 90 minutes).
But despite Kane failing to register a shot on target in two successive games for club or country for the first time since November, Shaw insists the England skipper's pedigree cannot be questioned.
"There's no concern at all. Personally, I think he's the best striker in the world," Shaw said of the 2018 World Cup Golden Boot winner and three-time Premier League top scorer.
"He is a very important part of the team, in fact the most important part. I think whether he has not been at his best or not he is a massive part and a crucial player for us.
"We need him whether his performances are as people expected or not, but this happens in tournament football.
"You can score a goal at any moment and he is such a crucial player – not just on the pitch but off the pitch. He has got all of our backing and I'm not worried at all."
England were frustrated by spirited rivals Scotland on Friday in the first goalless match between the sides at Wembley in 33 meetings.
The Three Lions are behind the Czechs on goal difference ahead of Tuesday's match, meaning a win is required if they are to finish top.
Following criticism on the back of the toothless display against Scotland, Shaw has put the stalemate into perspective with England as good as assured of a last-16 spot.
"There is no denying that there is a lot of disappointment," he said.
"We would have liked to win the game but you have to look at it in the way of another point in the right direction.
"If it was the other way round, we drew with Croatia and won today, it would have been four points still so we have to keep positive.
"I think there should always be expectation, the team we have, the talent is very strong.
"Of course we can take the expectation but maybe this result brought us back down to earth to make us realise it is not going to be easy."
England, who have never made it beyond the semi-finals of the European Championships, are on course to meet either Portugal, France, Germany or Hungary in the next round.
Taking positives from a 14th clean sheet in 18 matches for England in all competitions, Shaw added: "Our aim is to be here for seven games.
"We will sit down and watch the game back and analyze what we want to do better because there are things we could have done better as a team.
"Maybe in this game we weren't at our best and that shows, but it is another clean sheet.
"We still have another big game on Tuesday and we have to forget about this one and be ready."