Diego Milito struck the winner for Inter and Mourinho said: "Roma lost their heads when they realised that they had no chance of getting back into it and Totti in particular lost his head at the end. At that stage, the game was over."
Mourinho is heading towards an historic Treble, as Inter are also in the Champions League Final and leading the Scudetto race.
"Unlike after the Barcelona win, I will not ask the fans to come wait for the team at the airport. These people need a rest!
"Now there are three games where we can win another two trophies. We saw today that the team pushes to the end and gives everything it has. We will continue fighting to the last minute for these dreams.
"As I said in Barcelona, I want the Champions to be a dream for my side and not an obsession for us and our fans."