Ferguson is set for his final game in charge at Old Trafford on Sunday after nearly 27 years at the helm.
Carrick has played under the 71-year-old Scot since moving from Tottenham in 2006 and the England star told the BBC: "He is arguably the best manager of all time so for him to be sitting in the changing room and telling us it was his time to retire, it was quite an emotional time.
"I am grateful to have been able to play in one of his teams and play for this
great club. He is an incredible manager and an incredible man. His man-management, his hunger for success, his drive and desire makes him a one-off.
"Everyone is still coming to terms with the fact he is leaving and and a new manager is coming in. It has been a strange week to say the least. The initial thoughts were really disappointed and quite gutted when the manager told us as a team. It was quite sad in the dressing room.
"Plenty of people can have success over a short time but to keep evolving and changing his team and changing his approach to management is sensational and will never be repeated."
With Everton boss David Moyes picking up the reins for next season, Carrick is upbeat over the future of the club.
"I am very, very excited, very much looking forward to moving on to a new
chapter with the club and in my career," the 31-year-old added.
"David has done an unbelievable job at Everton over a long period of time to keep them up there challenging for Europe. He hasn't had the money of the top four or five clubs but he has always put a team out there to challenge.
"I am sure he will come here and have a successful time. He will not have to change things overnight because things have gone well of late, but he is his own man and we will all be right behind him as players."