Ronaldo hit a hat-trick as Real went through to the next round. Madrid started the night 2-1 behind against Celta Vigo but Ronaldo got them out of trouble with a brilliant treble in a 4-0 win, just two days after missing out on the Ballon D'or award to Lionel Messi for the fourth year in a row.
Progression in the cup was vital for Mourinho, who has lost the support of some of the fans of late owing to their capitulation in the title race and his decision to drop goalkeeper Iker Casillas.
According to Ronaldo, though, his fellow Portuguese deserves the support of all at the club. "I know him and he is a great professional. He is in charge and we have to respect his decisions," he said on realmadrid.com.
The support for Ronaldo and his team-mates was noticeable and Ronaldo is grateful to the supporters for their unity.
"I have to thank the fans, they are with the team. I am very happy about that," he said. "When people support me I feel better, more motivated and happy and also play better.
"I said it two weeks ago, I'm very happy. Not only in our own stadium, away too, and it motivates me to do better."
For Mourinho's assistant, Aitor Karanka, it was a case of business as usual last night, with Casillas back between the sticks and Ronaldo scoring goals.
"It is something that we have talked about since we've come back from holidays," said Karanka.
"Casillas has made good saves, Cristiano has scored three goals and that's what we ask of our players, that they are at the highest level. We work to pick the 11 that will give the best performance."
Mourinho rarely looked happy on the bench, suggesting he is feeling the heat of the current situation. He opted not to attend the Ballon D'or ceremony, choosing to spend time coaching his son's team instead, and Karanka defended the decision which has attracted some criticism.
"The manager said it, the fans do what they believe. He is in charge of working and getting the best for Real Madrid," he said.
"Being with him you are aware of what he does. And if the fans whistle it's because they are not happy. We are here to work and that's the way we've done it for the last two-and-a-half years."