Reports emerged that he had been seen driving away from the stadium in the hours before kick-off but Mourinho revealed a knee injury had kept him out.
"He's injured. He was injured, he was injured in the Friday training session and Saturday couldn't train", Mourinho said.
Explaining his vision for next term, the Portuguese said: "Moving forward I will organise my coaching staff in a way where the assistant manager figure doesn't exist".
Mourinho hinted last week Lukaku may only be fit enough for a place on the bench at Wembley next Saturday.
After the victory in the Reds' last Premier League game of the season, secured by Marcus Rashford's first-half goal, the players thanked the fans during their traditional lap of honour and captain Carrick addressed them in an on-pitch speech.
"In the future, when he has his badges, when he has his pro license". We spend more time with each other than we do with anyone else in our lives.
It is believed that Faria is looking to kick-start his managerial career in the 2018-19 season, but that leaves United without an assistant manager and Mourinho without his second-hand man.
"I don't think it makes sense when Rui is leaving after 17 years".
"I think we arrived at a hard time for the club. We had better performances than results", he said.
"We were always favourites to go there and win and obviously, as the years have gone by, they have developed and spent more money and they've obviously improved an very bad lot".
"I've already spoken many times with the owner. I don't know if he will be fit for the final".
"But I am going to improve my staff in the performance level and in relation to the tactical work".