Morata marked his first competitive start for Spain with the game's only goal, which settled a tight contest in Seville on Friday.
The Juventus forward was involved from the beginning after Diego Costa withdrew from the squad with a hamstring problem.
And he said the experience of playing - and scoring - was tough, but would drive him in the coming months.
"It was a difficult game," Morata said afterwards. "They are very tough, very physical.
"It wasn't my best game. But now I just need to keep working to get another chance in the team."
Morata has now scored in three successive games in all competitions.
Spain moved three points ahead of Ukraine with their victory, but are still three adrift of Group C leaders Slovakia who have won all five of their matches.
