The fullback admits that Les Bleus caused La Roja serious problems after the interval, but rued missed opportunities in the first period.
Real Madrid star Sergio Ramos put La Roja ahead early on in the tie, before Olivier Giroud leveled in the fourth minute of added-on time in the second period.
"The team is hungry and we tried to win against France," Alba told reporters. "But nothing has been decided, [and] there are more rivals we can make things difficult for.
"We controlled the first half, we missed and penalty and that was all very expensive. During the second period France were very strong, although I do not know whether it was down to fatigue."
The European rivals now share top spot in Group I, with Spain ahead on goal difference.
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