The current World Cup and European Championship holders find themselves second in World Cup qualifying Group I following consecutive draws against France and, on Friday, Finland.
Sergio Ramos scored to put Spain on their way in the second half in Gijon before Teemu Pukki scored a shock equaliser with 11 minutes left.
The draw means Vicente Del Bosque's side are two points behind leaders France, and with only one team guaranteed a spot for next year's finals Tuesday's game in Paris could be vital.
"Yes we made mistakes, we have dropped four points, but that happens in football," Arsenal player Cazorla said, according to AS.
"Those dropped points must be added in France to regain first place.
"It makes no sense today to doubt this team. The team is hungry, wants to keep winning titles and you cannot talk about the end of a cycle."
France's only dropped points came in their 1-1 draw in Spain last October and they approach the Spain game off the back of a comfortable 3-1 win against Georgia.
"The problem is we have less margin for error, but we always go out to win. We are aware that we have to make a great game against a team that is in a great moment," Cazorla added.
"In the last game we lacked things, we have to have more options."