After watching his new signing in action for the first time, the Portuguese coach described the striker as a "fantastic addition" to the Red Devils squad and hailed the role he played in their second goal.
"Alexis Sanchez is a fantastic addition, everyone is happy that he comes. Good players want good players. The question is always which one is going to be left out, it is not about that for us," BBC Sport quotes Mourinho as saying.
"We have a fantastic group of attacking players and he is another one with more maturity and experience. His choice for the second goal is a choice that a player like Marcus Rashford is too nervous to make that kind of decision. He brings maturity and class."
The United coach also admitted that Yeovil caused his side a few problems on the night, particularly during the first half.
"These matches are difficult if the attitude is not correct. In the first half they gave us a difficult time, pressing and aggressive on the ball and on the shinpads. I could hear Darren Way on the touchline, he knew what he was saying, they were organised," he said.
"But in the second half we had control of the game and had more space and more quality, we killed the game."
The result ensures that United will be included in the draw for the fifth round of the FA Cup.