Giggs left United at the weekend after almost 29 years at the club in the hope of furthering his coaching ambitions elsewhere.
The Welshman, who ended his glittering playing career in 2014, had spent two years as assistant boss to Louis van Gaal but opted not to continue under his successor Mourinho.
Mourinho, speaking in his first press conference since his appointment in May, wanted to dismiss the theory he was reluctant to work with Giggs.
He said: "It is not my responsibility that Ryan is not in the club
The job Ryan wanted is the job the club decided to give me
It is not my fault
Ryan wanted to be Man United manager."
The issue was one of a number of subjects former Chelsea boss Mourinho confronted in a confident performance before the media.
United have not challenged for the Premier League title and have twice missed out on Champions League qualification since Sir Alex Ferguson retired in 2013, but Mourinho is determined to get back to those levels.
The Portuguese said: "We have to make sure in July 2017..
this club is where it has to be, which is obviously the Champions League.
"But it would be pragmatic to say, 'Let's work, let's try to be back to the Champions League, let's try to be back to the top four, let's try to do well in the Europa League'
I want more than that
I prefer to be more aggressive, to say, 'We want to win'.
"I want everything
I want to win matches, I want to play well, I want to play young players, I want to score goals, I want to not concede goals.
"The last three years are to forget
I don't want the players to think to do better is to finish fourth
Finishing fourth is not the aim."
Mourinho is returning to management after being sacked by Chelsea last December following a spectacular slump in fortunes
He had won the Premier League, his third in England, just seven months earlier.
The 53-year-old insists he is not out to prove a point.
In a remark that could be interpreted as a dig at old adversary Arsene Wenger, the Arsenal manager who last won the title in 2004, Mourinho said: "There are some managers that the last time they won a title was 10 years ago
Some of them the last time they won a title was never.
"The last time I won a title was one year ago
It was not 10 years ago or 15 years ago, so if I have a lot to prove, imagine the others.
"I feel I have to prove, not to the others, but to myself
The reality is for the last five months (at Chelsea) I was in trouble
The first month was fine, the second not so good and after that it was a disaster."
Mourinho added that he felt Wayne Rooney's best position remained as a striker, not as he played latterly under Van Gaal and for England at Euro 2016, as a midfielder.
"He will never be someone playing 50 metres away from the goal," he said.
Mourinho came prepared with a list of 49 players he claimed to have promoted from youth ranks during his career, to combat claims he overlooks Academy graduates.
"One lie repeated many times sometimes looks true but it will never be true," he said.
Mourinho has also revealed United's England trio of Rooney, Chris Smalling and Marcus Rashford will be on the club's tour of China later this month but not feature in either of the scheduled games - friendlies against Borussia Dortmund and Manchester City on July 22 and 25 respectively.
Source : PA
Source: PA