Mourinho watched on as his side failed to break down a stubborn Chelsea side who won the cup through a first half Eden Hazard penalty.
Lukaku was only fit enough for the bench and came on for the final 17 minutes of action while Fellaini was not in the squad.
And Mourinho is said to be raging at the two players believing they were saving themselves for the World Cup rather than putting their bodies on the line for Manchester United.
Lukaku had been out injured since the 2-1 win over Arsenal at the end of April while Fellaini has been in and out of fitness.
Mourinho thinks both could have played a bigger part at Wembley and failed to show enough fight.
“When a player tells you he is not ready to start, then the question is how many minutes do you think you can play,” said Mourinho when asked about Lukaku afterwards.
“How can I convince a player who tells me he is not ready to play?”
Fellaini was expected to be involved despite his recent lay-off but was not in the squad and now appears to have played his last game for the club.