The Atletico Madrid striker was dogged by a hamstring complaint towards the end of their domestic campaign and his presence in Vicente del Bosque's squad looked in doubt.
However, he came through 74 minutes of Spain's 2-0 win over El Salvador unscathed at the weekend as the World Cup holders completed their build-up to Brazil.
Ahead of their opening game against the Netherlands on Friday, where he could lead the line, Costa reassured fans of his fitness.
"I needed the game against El Salvador. Before that I felt OK, but I relapsed," he explained.
"Now I'm fine, and there won't be a problem with the first match.
"It's normal to feel (anxiety). We're training to get better and be at our peak fitness.
"The climate will take its toll, because we play most of our season in the winter. It’s important the pitches are well watered."
Costa switched his national allegiance from Brazil to Spain late last year having gained dual nationality.
Despite turning his back on Brazil, for whom he made two friendly outings early in 2013, Costa says he has been welcomed warmly in his homeland.
"Things are going well. I've been treated as I hoped. I've been supported by a lot of people who understand what happened," he added.
"My parents are really happy I'm here, close to them. They support my decision."
