The Spaniard, who scored his sixth league goal of the season against Almeria at the weekend, is also confident that Los Blancos will overcome Barcelona in the final of the Copa del Rey on Wednesday.
"It's a privilege to wear this shirt," he told reporters. "I'm going to give everything for this shirt. Next it's the final against our biggest rivals and we'll do everything we can to try and win. If we stick together we'll achieve that."
Morata has scored a goal every 47 minutes in the league for Madrid this season.