Mourinho gave his first news conference Tuesday following his appointment as United manager
in May -- nearly seven months on from his sacking at Chelsea.
The Portuguese was dismissed by Chelsea in December
after his side lost nine of its opening 16 league games of the new season, despite having coasted to the 2014-15 Premier League title.
While the 53-year-old was in relaxed mood at his official unveiling, he couldn't resist having a dig at Arsenal manager and long-time rival Arsene Wenger, who last won the title in 2004, when asked if he felt any pressure following his premature exit at Chelsea.
"Some managers, the last time they won a title was 10 years ago," said Mourinho. "Some of them, never. The last time I won a title was a year ago. So if I have a lot to prove, imagine the others.
"The reality is it [having a point to prove] was never important for me. I play against myself. I have to prove not to the others but to myself -- that's my nature."
The rivalry between Mourinho and Wenger is well documented, with the pair having feuded ever since the Portuguese's first arrival at Chelsea in 2004.
It arguably reached its peak in 2014 when Mourinho referred to the Frenchman as a "specialist in failure," with Arsenal at the time not having won a trophy since the FA Cup in 2005.
Mourinho will also renew his rivalry with new Manchester City manager Pep Guardiola next season, with the duo having clashed during their time as respective Real Madrid and Barcelona bosses in Spain.
But while the new United manager has history with both Wenger and Guardiola, he says he will only be concentrating on his own work over the coming months.
"To speak about one manager, one club, one enemy -- I don't think it's right," Mourinho said. "In the Premier League, if you focus too much on one opponent, the others are laughing.
"It is not Spain or Italy. So I am not going to be a part of it. I am Manchester United manager and I have respect for every club. I have the same respect for every manager."
Glory days to return at United?
Despite his disappointing end to second spell as Chelsea manager, Mourinho arrives at Old Trafford with one of the best managerial CVs in the modern game.
The Portuguese has two European Champions League titles to his name, while he has also won a host of league titles in Portugal, England, Italy and Spain.
With United having suffered in recent seasons following the retirement of Sir Alex Ferguson in 2013 -- finishing seventh, fourth and fifth in the league since then -- the club will be hoping Mourinho can restore it to its former glories.
"My history in the last 10 years or more was to live with big club's expectations," Mourinho said.
"It comes at a right moment in my career. I have great motivation, I am where I want to be. I want to be in this club, this country, in the Premier League."
"The club is much more important than myself," he added. "Manchester United is a Champions League club and in July 2017, instead of waiting for the Europa League, we have to make sure this club is where it has to be. That is obviously in the Champions League."
As to what style of football United would play, Mourinho twice referenced the word "aggressive" in one answer.
"I prefer to be more aggressive and say we want to win. What is playing well? It is scoring more goals than the opponents, conceding less, making your fans proud because you give everything and you win.
"It is everything at the same time. It is an aggressive approach by myself. I want everything. Of course we are not going to get everything but we want to."