The German international has come in for some criticism from sections of the Spanish media following some below-average performances this season.
However, Ozil said that he remains confident in his own ability, while also feeling reassurance from Mourinho.
"I knew there would always be competition when I signed for Real," Ozil told Kicker. "My target is to concentrate on my task, to concentrate on my performance.
"I know what I am capable of, and have shown it on several occasions. In the end it's up to the coach, who starts. I get along great with Luka Modric, he is a super guy and player.
"The coach knows what I am capable of and I am thankful he's put confidence in me. It's like that in Spain. I've been here for three years now, and know the media. You have to cope with that, even if it's over the top at times."
The 23-year-old joined Los Blancos from Werder Bremen in 2010.