Inter entertain United at the San Siro on Tuesday knowing it is almost half a century since they last won the competition, and in the knowledge they were eliminated by Sir Alex Ferguson's men at the quarter-final stage in 1999 when the Red Devils went on to win the trophy.
But, despite the Premier League's apparent superiority to Serie A, Mourinho cannot wait.
"I am actually pleased about that because my team plays better under pressure against the best teams," he told MUTV.
"We have always done well against Milan or Roma or Juve but sometimes against small teams we are not the same.
"We have to be at our best if we want to win the tie so I am happy to have such a big team."
Mourinho feels Inter deserve their fate because of a woeful end to the group phase that saw them collect just one point from their final three games, allowing Panathinaikos to seal a meeting with Villarreal, who finished runners-up to United.
It is now 18 months since Mourinho was unceremoniously dumped by Chelsea.
Many pundits now believe he is the number one candidate to replace Sir Alex Ferguson when the Scot eventually calls time on his amazing career.
He admits life in Italy is not the same as in England, although he does feel he is embarking on the biggest challenge of his entire career.
"I used to say the Premier League was more about heart and emotion," he said. "Serie A is more about brains and tactics.
"Every team in Italy is strong defensively. Every game is about tactics.
"It is not as beautiful as the Premier League. That is one of the reasons why the Premier League is loved around the world and Serie A is loved in Italy.
"It is more about the mentality and culture. But this is a really big challenge, the biggest of my career."