The defeat in Group D was the country's first loss at a European Championship since 2004. The champions finished second in the group behind Croatia and now face Italy in Paris on Monday.
"We must forget about this loss," winger Nolito told Marca. "This is a European Championship and we can't think about what we missed but rather look ahead."
Spain had dominated their first two opponents in the group, beating the Czech Republic 1-0 and Turkey 3-0.
But against Croatia, captain Sergio Ramos had a penalty saved by keeper Danijel Subasic midway through the second half before Ivan Perisic scored a late winner.
"Had we scored the penalty, it would have been a different story," Juanfran said. "Perhaps we needed a game like this one. But we are not worried, we are united and much stronger than ever for Monday's game."
Spain have bounced back from defeats before. They lost their opening game against Switzerland at the 2010 World Cup but went on to lift the trophy.
"It's better to lose now," Nolito said. "There are always lessons to be learned. We don't fear anyone and we have to be ready to compete against the best. Italy are tough opponents but I'm sure they will respect us, just as we respect them."
(Reporting by Adriana Garcia. Editing by Adrian Warner.)
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