Alexis Sanchez, 29, made his Manchester United debut in the 4-0 win over Yeovil on Friday night.
The former Arsenal star, who swapped places with Henrikh Mkhitaryan at Old Trafford this week, earned an assist in the romp at Huish Park.
Sanchez started up front alongside Marcus Rashford, whose place in the United first team is now under threat from the Chilean’s arrival.
But manager Mourinho insists Rashford – and his other strikers at Old Trafford – can learn from the ex-Barcelona star.
“Alexis Sanchez is a fantastic addition, everyone is happy that he comes,” Mourinho said.
“Good players want good players.
“The question is always which one is going to be left out, it is not about that for us.
“We have a fantastic group of attacking players and he is another one with more maturity and experience.”
Sanchez provided Ander Herrera with the second goal when playing the Spaniard through after starting a counter attack.
Mourinho said of the goal: “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.”
Manchester United are through to the fifth round of the FA Cup, with the majority of teams playing their fourth-round games tomorrow.
Speaking of the win, Mourinho added: “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 (Yeovil boss) Darren Way on the touchline, he knew what he was saying, they were organised.
“But in the second half we had control of the game and had more space and more quality, we killed the game.”
Jesse Lingard came off the bench to score United’s third goal, before Romelu Lukaku wrapped up the win in stoppage time.
Lingard said: “Our attitude was spot on, it was always going to be tough.
“We adapted well to the ground and all made an impact.
“The FA Cup is very important, it’s great to win trophies, that’s what we are here for.”
And Herrera, who scored his first goal since April last year, said: “We had to work very hard, it’s not easy to come here.
“The passion they put in for every ball made it tricky but we took it very seriously.
“Alexis Sanchez can play everywhere, he’s fantastic. The attitude he shows, he fights for every ball.
“He’s a star and it’s amazing to have him with us. This is a team and today we did it well.”