The Nerazzurri were crowned Italian champions for the fifth successive season after claiming a nervy 1-0 victory over Siena on Sunday.
AS Roma, who were two points behind Inter, defeated Chievo 2-0 but their victory counted for nothing at the end.
"It was difficult but I had never had this experience of winning a championship at the last minute," Portuguese coach Mourinho said.
"I had won it at home, in the hotel, with three or four games left, always with great tranquility. This is a new experience, which I hope is not repeated."
Inter, who have also won the Italian Cup, have a chance to complete an unprecedented treble.
They face German giants Bayern Munich in the Champions League final on Saturday.
"The championship is over now. Winning the Scudetto and the Coppa Italia is always fantastic," Mourinho, whose future remains uncertain, added.
"Bayern Munich have done it too, but only one of us can win the Champions League.
"Am I already thinking about the game on 22 May? I don't know, but in this moment I don't have the strength to go on the bus and watch Bayern on DVD. But I will be back to work tomorrow."