The 30-year-old netted a double as Didier Deschamps' side twice came from behind, eventually winning 4-2 against their Group I rivals.
"I'm not the saviour," Ribery told reporters.
"I scored at the right time, when France needed me to score. We're happy to have put in a great second half.
"We'd not scored for a while and we were strong mentally. After going 2-1 behind we were fortunate enough to equalise quickly."
The Bayern Munich star, who recently won Uefa's Best Player in Europe award, was an injury concern before the game, but he says he always felt he would take part in the contest.
"Some other players might not have given it a go with the injury I was carrying but I like to contribute what I can," he added.
"The physio did a great job and I knew from the eve of the game that it would be okay."
Deschamps, meanwhile, lauded Ribery's performance in a difficult game for his side.
"We've got a great player in Franck Ribery and he confirmed that here," he added.
"It was tough and we didn't have many chances in the first half. We scored early in the second and were in the midst of a good spell when we conceded a second goal that hurt us.
"We were 2-1 down in the 57th minute and a long way away from our objective. We scored four goals and that's something France have not done since 2009.
"The importance of getting a result had made us tense but we were much better in the second half in all departments of the game."