Payet has praised France’s ability to win matches in the late stages of a match.
The midfielder struck in the 96th minute, after Griezmann broke the deadlock in the 90th minute, as les bleus won 2-0 and qualified for the last 16.
But the West Ham star says France have proven time and time again that they can win a game at any time.
“What’s great is this is nothing new, since March and against Holland we have shown that we can always win games late on, we’ve been able to score in stoppage time since the start of the competition,” Payet told reporters.
“We had to be patient, we tried to go through the middle in the first half but used the width in the second. The subs made the difference tonight and we were able to come up with the goods.”
But while Payet believes in France’s ability to win games at any stage, he was relieved to see Griezmann finally score the opener.
“It was a special feeling, we said that last week that everyone was important in the squad and that was the best way of showing it,” he said.
“Union and team spirit were important tonight. A lot of people were doubting us but we won the game.”
Payet also hailed France’s fans after he and his team-mates secured their progression to the last-16 of the tournament.
“Once again I made the difference tonight and I have known for a while that my country is right behind me and there is a particularly fervent support for Les Bleus in the country,” he added.
“They are very proud that France have made it through to the last 16.”