Mourinho tells Rooney to make up his mind if he wants to leave United for Chelsea
The Londoners have been linked with the unsettled England international throughout the summer transfer window but United have been steadfast in their determination not to sell.
Mourinho is still keen on the player but admits it is almost time to bring the saga to a close and wants the player to speak out.
Mourinho, speaking in the post-match press conference, said: "I think the person that started the story has to finish the story.
"A club like us, a manager like me and the people that work in the club with me, we are not silly to try to get a player from a big club, a club that doesn't sell what they don't want to sell.
"We are not silly to try to something if somebody didn't start it.
"It is time for the good of everyone to finish the story, to one side or the other side."
When asked how he knew Rooney had been agitating for a move, Mourinho said: "Because I know."
Rooney, 27, received a good reception from the United fans before kick-off and Mourinho suggested he would not be surprised if such support changed the player's mind.
He said: "The most important thing is that he played very well. He was a real professional.
"He played for his club, played for the club that pays him, tried to win, tried to score. He was fantastic.
"After that, if he wants to leave, he has to say - or he decides now that he doesn't want to leave anymore.
"But I praise him. He played a fantastic match in these difficult circumstances.
"Many players in this situation can't express themselves on the pitch. They don't feel enough confidence or they cannot forget what is behind (them)."
Specifically on the crowd, Mourinho said: "In other countries it wouldn't be possible, in other clubs it wouldn't be possible.
"It doesn't matter the player you are, they don't want you.
"But they gave him fantastic support, it was good, it was nice - very English."
With just a week until the transfer deadline Mourinho said he might only give Rooney another "24, 48 hours" to decide before moving on to different targets.
"We are going to close another player if he is not coming," he said.
Mourinho's counterpart David Moyes, however, remained unmoved.
The Scot said it would "illegal" for Mourinho to make any request to Rooney.
Moyes was delighted with Rooney's display on his first start of the season and praised the crowd for their response to him.
Moyes said: "I was very pleased with his performance and I was very pleased with the reaction from the crowd.
"I have got to say, I didn't think it was unexpected. I don't know how many times I have to say it, he has been great in training.
"I think anyone who looked at him might have seen a slightly leaner-looking Wayne.
"I said to him he might only play 60 minutes but I thought he worked back, he tackled, he chased when we needed it.
"I think Wayne has a positive mind at the moment. I don't think he needs to change.
"I think his performance tonight said enough. I think his actions tonight showed what he thought."
Moyes' former club rejected a £28million joint bid for the duo last week and Everton boss Roberto Martinez has since criticised his Goodison Park predecessor.
Moyes said: "I never released we had made the first bid and I certainly wouldn't release it if we made a second bid.
"Maybe you should ask Everton, they might tell you that."
When asked if United had made a bid on Monday, Moyes said: "No.
"I have just said Manchester United are always interested in the best players.
"The board and myself would always be looking to sign who we think are the best players, whoever they are."
Mourinho also rubbished suggestions he might be prepared to let playmaker Juan Mata leave Stamford Bridge.
He said: "He is very important for me and very important for Chelsea.
"The stories that are coming out are nonsense stories. He goes nowhere."