Franck Ribery, Blaise Matuidi and Raphael Varane all squandered goalscoring opportunities as did Karim Benzema, the Real Madrid forward again booed off after extending his international goal drought to 12 matches.
It meant Pedro's goal after 58 minutes was enough to secure three points for Vicente Del Bosque's side who will guarantee their place in Brazil next year if they can take seven points from their final three qualifiers.
To compound matters for France, who face having to go through a play-off if they are to reach South America, Paul Pogba was sent off on 78 minutes after picking up two yellow cards.
Manager Deschamps pointed to his side's lack of clinical finishing although he also underlined the quality of the opposition.
He said: "Spain had more possession but that is not a surprise.
"What is the most annoying thing is that we had more opportunities than them and that's where we were guilty although in the first half we defended well.
"But do not forget the team we faced. We battled well but the result is a disappointment.
"Even with 10 men, we managed to be dangerous but up against such an opponent with skill and experience, (you need) favourable circumstances but that was not the case."
The former Marseille, Nantes and Juventus midfielder added: "In a collective performance, I will not highlight those that were not successful, but there was such a quality opponent that it was very difficult to defend against such players.
"Up front, there was more control and experience.
"This is a team that has three titles in their pockets, they are the best."
Benzema is enduring a torrid time on the international stage but with more than 100 caps himself, Deschamps is well qualified to comment.
"There is a lot of debate unfortunately but it does not help him and it does not help us," he said.
"Karim was part of the team and did good things.
"He did not find the way to goal but he was able to be part of the game and made things interesting."