"But it's true that in worldwide competition, along with Euro 2012 and the World Cup in Brazil, it's perhaps my best match".
Hosts France beat Iceland 5-2 in Sunday's quarter-final at the Stade de France to set up a last-four tie with the world champions, who beat Italy on penalties on Saturday after a 1-1 draw.
Olivier Giroud scored a brace to go with goals from Griezmann, Paul Pogba and Dimitri Payet in Paris.
"Now we have gotten a taste of being at the big stage, we love it and we belong here", said Halldorsson.
"It is going to be very tough, but we are going to go all in and give it all we have to qualify (for the World Cup)".
"I think the fans, how appreciative they are to the players, and what is also fantastic is that the players showed their appreciation to the fans".
"I don't know if that's my best performance for France because I've played some other good games but in a major tournament, such as Euro 2012 and the World Cup in Brazil, that is my best. They had a wonderful Euro", added Giroud, who was brought off after his second goal to avoid getting a new yellow card that would have led to a suspension.
Didier Deschamps' side will now meet Germany in Marseille on Thursday.
"We have a lot of desire to get our own back for what happened at the World Cup", Giroud said of the quarterfinal loss to eventual champion Germany two years ago. We're disappointed but still incredibly proud.
At the other end, Lyon defender Samuel Umtiti impressed on his worldwide debut, much to Deschamps' delight.
Iceland joint-manager Lars Lagerback rued what he called the "silly mistakes" of his side in the first-half, but overall has only happy memories of the tournament.
"He is one of the guys that took us to France and to the quarter-finals".
The Arsenal striker remained just onside as he ran onto Blaise Matuidi's through-ball, allowing it to bounce before lashing it through the legs of goalkeeper Hannes Thor Halldorsson. Ultimately, though, Iceland managed to pull a couple back.
Then, Pogba soared above Jon Dadi Bodvarsson to meet Griezmann's corner and send a powerful header into the top corner in the 20th.
Bdvarsson nearly conjured a response, firing over from close range following an Aron Gunnarsson long throw, but this was a day when chances had to be taken. But Les Bleus had wrapped up their place in the last four by half-time.
Iceland were rewarded for their perseverance though as they grabbed a second goal when Bjarnason headed in Ari Skulason's cross on 84 minutes.