Didier Deschamps' men failed to impress in the group stages, before recording a hard-fought victory over Republic of Ireland in the round of 16.
The tournament hosts were in fine form on Sunday, though, as France comfortably brushed Iceland aside to set up a semi-final showdown against Germany.
"This was our best performance this tournament," Payet, who scored his side's third goal, 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."
France meet Germany next with the world champions expected to miss a number of key players.
Mats Hummels is unavailable due to suspension, Mario Gomez is out of action due to injury, while Bastian Schweinsteiger and Sami Khedira are both doubtful.
Nevertheless, Payet is adamant Germany remain a major force even without a number of regulars.
"Germany will not be weakened," he insisted.
"They are the reigning world champions."
Antoine Griezmann played a pivotal role in France's win with one goal and two assists, but the Atletico Madrid forward is not getting carried away, urging his team-mates to keep pushing for more.
"We wanted to make a great start and we did just that," Griezmann stated.
"It's a shame that we conceded twice. But we have to keep going on the same path. We have to give our all in the semi-final against Germany in front of our own fans. We will give everything to get to the final."