The 30-year-old was demoted to the bench in the 4-1 win over Leicester with first-half goals from Chris Smalling, Juan Mata, Marcus Rashford and Paul Pogba sealing the win at Old Trafford.
Rooney came on as an 83rd-minute substitute for Rashford, but his position on the bench sparked fresh doubt over his future at United.
However, Mourinho has quashed any uncertainty over Rooney's position at the club by insisting that he remains a key part of his squad.
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Manchester United captain Wayne Rooney started on the bench in the 4-1 win over Leicester
"Wayne Rooney is a big player for me, United and this country. he is my man, I trust him completely. He is happy," Mourinho said.
The 53-year-old also opened up about the win over the defending Premier League champions.
"It was a very good performance and result. It is not easy against them and not easy to win in the style that we did.
"In the second half it was more about control - we wanted a little bit more - but Ranieri was very good to read his options and keep some balance. It was a choice of losing heavily or with some control over the scoreline.
"Today we had intensity movement and dynamism. To be back home and beat the champions is good. Last season we couldn't beat them and this season we have beaten them twice already.
"We have lost six points in the Premier League. We have four victories which is really important. Today it is about the security and the happiness of the fans, I don't know when the last time that they had such a scoreline at half time."
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