The former Chelsea boss, who was announced as Louis van Gaal's replacement in May, kicked off his pre-season training program with certain senior squad members last week Wednesday.
"It's been very good," Carrick told MUTV. "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!
"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."
The 34-year-old and the United management team put an end to speculation over his future at Old Trafford by agreeing to a one-year contract extension in March.
"I'm delighted to be here," Carrick said. "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."