Man-of the-match Olivier Giroud hailed the team performance, but warned that they would still need to improve at the back against Germany.
"They are the best team in Europe and in the world and the only ones totally controlling the situation, with technical quality everywhere, from the goalkeeper to the forwards", Deschamps said. He was joined on the scoresheet by Paul Pogba, Dimitri Payet and Griezmann.
"What we are going to remember is that they are the world champions".
The night began with rain descending on the field and the Viking slow capping ritual, with its "Huh" chant, booming around the stadium from the Iceland fans. We are used to making bad starts to matches and we changed that. We know what to expect, we know they have qualities.
Deschamps withdrew Giroud and key defender Laurent Koscielny during the Iceland game as they were at risk of suffering the same fate.
"Hopefully the FA in Iceland and clubs can take this in and perhaps use the income from this tournament and put it into a project to help develop young players".
"We have probably 10-15 players who are at a really good age and we'll be looking forward to the World Cup qualifiers which aren't too far away".
It was a totally dominating French performance as Olivier Giroud opened the scoring before Pogba added a second via a header from a corner, Payet scored a third with his weaker foot and Griezmann lobbed the goalie to make it four on the stroke of half-time.
"It's been a fantastic journey for me and I feel all the positivity and interest deep in my heart", he said. "But we are there in the final four and we'll give it our all", said Deschamps.
Coming into the game, Iceland was praised for a rigidly well-organized defence while France had found first-half goals hard to come by, with its previous six coming after the break. We made some silly mistakes, and we didn't do well as a team.
"If you look at the whole tournament, to reach the quarter-finals as a newcomer is absolutely fantastic".
With six minutes remaining, Bjarnason pulled another goal back for Iceland with a header but the tie, and Iceland's hopes of extending their dream run, were over.
It could be a shoot-out between Griezmann and Payet for the golden boot with Griezmann having netted four and Payet now on three after their goals in Paris - although Wales' Gareth Bale, who also has three, will want a say.