"They scored two goals over the course of the two games and we have to accept that, in football, the team that wins always deserves it but I don't think we should be negative about my team's display," stated Mourinho.
"We played a great match against a great team. We just lacked that little bit of luck you need to win, that little thing that makes that difference between winning and not winning.
"We went one down after a couple of minutes but we had three chances to score in the first half, more than our opponents, and we hit the bar from three metres out.
"In the second half we lost another goal but we continued to play and we showed great character."
Mourinho is confident his side will bounce back from the disappointment and go on to seal a fourth consecutive Serie A title.
Mourinho's Inter team are seven points clear in Serie A
They are currently top of the table, seven points clear of second-placed Juventus.
"We have not been good enough to win the Champions League but we are good enough to win the Scudetto and I'm sure we will go on and win it," he said.
Mourinho also revealed he would be telling Inter president Massimo Moratti what needs to be done to make Inter a match for the likes of United.
"You can't just turn up and expect to win the Champions League just like that," he commented.
"One way is to spend a huge amount of money, which we know is not realistic in the current climate. The second way is to build a team over the course of time.
"Chelsea lost three semis before getting to last year's final. It is a process and getting to the top is a consequence of the hard work you put in."
United can tighten their grip on the Premier League by beating title rivals Liverpool at Old Trafford on Saturday.
But former United goalkeeping legend Peter Schmeichel told BBC Sport that good as the current side is, a clean sweep of five trophies may prove to be just that bit too much for them.
"I think it's a dream that's not very realistic that it's going to happen," said Schmeichel, who played in the 1999 treble-winning team.
"I remember 10 years ago the kind of luck we had.
"So many things must go your way. I hope they'll do it but it's a long shot."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.