The midfielder, who signed a one-year deal with the club last month, returned to Carrington on 6 July to begin work with the 53-year-old.
Manchester United visit Wigan Athletic on Saturday for their first pre-season match before jetting off to China to face Manchester City, Borussia Dortmund and Galatasaray later this month.
Speaking to ManUtd.com, Carrick reflected positively on Mourinho’s first week as manager.
“It’s been very good,” said Michael, when asked about how the first week under the 53-year-old had been.
“We came in last Wednesday and have done over a week with him now and it’s been enjoyable. The sessions are very good, it hasn’t broken us yet and hasn’t been as hard as you might think! [Laughs]
“There’s been a lot of football and fun at the right times, and I think everyone’s enjoying it. When you get a new manager, pre-season is always a little bit different because it’s a new personality and new ways. But you approach the season as any other and you’ve got to prepare yourself to be ready for the battle.
“That’s what the first few weeks of pre-season are for, to get that base of fitness and mentally prepare yourself for the year ahead.”
Asked how pleased he is to have penned a new contract, Carrick added: “I’m delighted to be here. I’ve been here quite some time now and I just love the place.
“It’s such a great place to come and work every day. I’ve still got that drive and desire to be successful and give everything I can, so hopefully this year will be a good one.”
As this United side attempts to gel under a new manager, Carrick’s presence is hugely valuable. He is one of the few players at the club who experienced the Sir Alex Ferguson era, meaning he possesses an almost unprecedented level of experience and understanding of what playing for United means.
His composure and ability to shape the speed of a contest, a quality that has served him so well down the years, will be vital in allowing Mourinho’s side to dominate big games. When deployed correctly, Carrick can put the opposition on the back-foot without even entering their half, such is his immense capacity to skilfully manipulate the ball and pick out teammates.