Morata has delivered a personal best haul of 20 goals back at Santiago Bernabeu but faces fierce competition for places from the likes of Cristiano Ronaldo and Karim Benzema.
Goal revealed earlier this week that United are considering an approach to bring him to England, and the 24-year-old concedes that he is looking for regular game time.
“I’m not thinking about vindicating myself,” Morata told reporters.
“I want to win the League and Champions League like everyone else.
“It’s going to be difficult, but if we win all our remaining games, we’ll be champions in two competitions.
“I’d like to play in every game, like everybody else. You always want to contribute wherever you are.
“I always want to go out and score, but there are times when you can’t.
“Playing less than I hoped? Sure, but I’m always ready for when the coach needs me and that’s the important thing.”
Morata has bettered the return of striking rival Benzema this season, with the Frenchman contributing 17 goals so far, but he is placing little importance on that record.
He added: “More goals than Benzema? The fans think this more than I do.
“I don’t think about scoring more goals than a team-mate, only to score. I’m at 20 and it’s a good number.”
Morata has also been linked with a cross-city switch to Atletico Madrid over recent weeks, with Diego Simeone reported to have sounded him out during a Champions League semi-final clash between the arch-rivals.
Both men have, however, sought to play down those claims.
In echoing Simeone, Morata said of the incident in question: “Talking to Simeone at the Bernabeu? It had nothing to do with football, we had a joke.”