Les Bleus bounced back from Friday's shock friendly defeat to Japan with a dramatic World Cup qualifying point in Madrid thanks to substitute Olivier Giroud's stoppage-time goal.
Menez told L'Equipe: "This could be the start of something. It's a turning point.
"We did not steal this draw. In the second half we were more relaxed and we created a lot of chances.
"We didn't let our heads drop and we battled until the end. It is pleasing to get our rewards. We showed that we too know how to play football."
Marseille's Mathieu Valbuena was more understated about the significance of a result which leaves the two sides level at the top of Group I on seven points.
"We got our reward because we did not let up," he said. "But we are not world champions, we are not European champions, we must not get carried away."
Valbuena was singled out by coach Didier Deschamps as a key figure in his side's comeback and he added: "The coach asked me to play as a 'number 10' between the lines. I tried to use my mobility, to ensure we got the ball because we did not have it very much in the first half."
Deschamps said: "Even before the match, I knew my players and I had confidence in them. We have quality.
"Being greedy, we could say we possibly could have won, but a minute and a half from the end we were on our way to losing.
"They came back very well. You can say 'why didn't they start like that?' but I knew that in the first half, we would have to defend. In the second half, we forced Spain to defend.
"Those who started put the hard work in and those who came on brought a lot to the game."
Spain took a first-half lead through defender Sergio Ramos but then saw Hugo Lloris save Cesc Fabregas' penalty to keep France in the game.
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