Eden Hazard's 22nd minute penalty proved the difference between the teams to ensure Mourinho's second season at Old Trafford ends without a trophy.
And as the Chelsea board deliberate over his future the Italian has told the club that an overhaul of the playing staff is required no matter who is in charge.
"I have a contract and I have committed to this club", he said.
"We'll see after the World Cup whether I am a Chelsea player for next year", said 26-year-old Belgium worldwide Courtois, who is out of contract at Stamford Bridge next summer.
Olivier Giroud improved the team greatly, but by the New Year, Chelsea's hopes of regaining the Premier League title were gone.
United are expected to spend big this summer in an attempt to challenge Manchester City for the Premier League title next season.
"I knew without a target man (it) would be hard for us", added Mourinho.
Back on the BBC, José was telling us that United deserved to win.
"I think you have to understand if in this season we had the maximum or not".
"I'm sure, if I was a guessing man, they obviously will have spoken, between the club and the manager". We couldn't finish in the top four, we don't have the Champions League next season, but at least we have something to celebrate with the fans.
Hazard was the catalyst for Chelsea's eighth FA Cup victory as the Belgium playmaker produced a virtuoso performance capped by his 22nd-minute victor. I congratulate [them] because I am a sportsman and they scored one more goal than us and they get the Cup. "I think now if you want to win something like the Ballon d'Or or the top-scorer (award), you need to be selfish". I'm the coach of a great, important club, in England and the world.
"When you look at it in terms of previous year, Premier League title, and then the FA Cup it's not too bad".
"I am quite curious because I can imagine if my team played like Chelsea did I can imagine what everyone would be saying".
Jones had United's best chance of the first half but headed wide at the back post as he tried to make amends for his earlier error.
Warriors rout Rockets in Game 3
Houston was coming off a morale-boosting victory in Game 2 that was believed to have re-injected some confidence back to the team. Whether they get a bucket or not, my job is to make it tough on them, and I did that really well Game 1.