The 21-year-old has risen through Real's youth system and made nine appearances in all competitions this season, all but one coming from the bench.
After an inauspicious start to the campaign from team-mate Karim Benzema, some supporters called for Morata to be given an opportunity to prove his worth in the starting XI.
Speaking at an Adidas publicity event, Morata said: "I'm not at all disappointed. Last year I played about 17 matches and this season I've played in nine already.
"I think I'll end up playing more than last year and if anything that means I'm improving, which is good.
"I'm young and there is no need to rush things because I'm at one of the best teams in the world. My time will come.
"I'm working hard, and I am just thinking about enjoying myself at this club and with our fans."
"We have to take it one match at a time and keep working as we are," he added. "There have been a lot of changes over the last year and we are gradually improving.
"I'm sure we we'll be in the fight for all of the titles."
