Kane had drawn England level with France in the quarter-final tie with a successful spot kick that saw him match Wayne Rooney's record haul of 53 goals.
He then had the chance to make it 2-2 late on after Mason Mount was fouled by Theo Hernandez in the area, but blazed his effort high over the crossbar as the Three Lions lost 2-1.
Despite the major miss, Conte expects his star man to recover quickly for the Boxing Day's clash at Brentford as the Premier League season resumes.
He said: "No, honestly [I am not worried] because we are talking about a world-class striker but at the same time, you know football is this.
"Football you can have exciting moments and you can also have a moment where you are a bit disappointed because you missed a second penalty. The first he scored.
"But me when I was a player, I never missed a penalty because I didn't kick. Never! Because I was a real disaster at it. But with a penalty I lost a World Cup against Brazil [in 1994] and you live this moment. You are really disappointed.
"For sure the first period you are sad but then you know that you have to move on. Football gives you the opportunity to have other chances to enjoy.
"Don't forgot we do this job and also we are really lucky because we can enjoy this sport. Football gives us the possibility to play in the sport we have a lot of passion for.
"Honestly I am not worried about him. I saw him very well in these two days with us."
Tottenham are currently fourth in the table but eight points behind leaders Arsenal. Conte's contract is set to expire after the end of the season, although Spurs do have the option to extend it by 12 months. Naturally, there is speculation over his future at the club.
"I think I would like also in the future to not speak about this matter in the press conference because I think it is much more important the game we are going to play," Conte said.
"In this case Brentford, but what I can tell you is I am really happy in the club, to work here and I have a really good relationship with the club."