Despite conceding two goals during the match, Payet was pleased to see France dominate in the early stages of the game.
"This was our best performance this tournament," the 29-year-old midfielder told reporters. "We managed to score a lot of goals, which was great. And it was important that we scored early on.
"We have a lot of quality in attack. We had a lot of chances, which allowed us to score. We were aware of Iceland's strength, but we were on top of our game."
Having got past a spirited Iceland side, France will be in for a huge challenge in the semi-finals as they face world champions Germany.
Germany, though, will be missing a number of key players for the match on Thursday as they will be without Mats Hummels, who has been suspended, while Mario Gotze will be sidelined due to an injury. Bastian Schweinsteiger and Sami Khedira meanwhile have been listed as doubtful for the match.
Despite this, Payet acknowledged that Germany will still give France a run for their money as they will be gunning to win their first European Championship title since 1996.
"Germany will not be weakened," Payet said. "They are the reigning world champions."