Since taking charge following Ruben Amorim's dismissal in January, Carrick has guided the club to seven wins in 10 matches, with just one defeat.
Under the former United and England midfielder, the Old Trafford club appear poised for a return to the Champions League next season and are third in the Premier League with seven games remaining in their campaign.
"From a personal view, he's the right man. He has a lot of experience, he knows the club and has the DNA. His relationship with every player is very good," Ivory Coast international Amad told reporters on Tuesday.
"Sometimes this kind of manager can bring the club where they belong. It's not the players who decide, but my honest opinion is we're really happy to have Michael Carrick as a manager."
Forward Bryan Mbeumo, signed from Brentford last year, echoed those sentiments, saying United's players had had a "good experience" working with Carrick.
"He knows how to talk to us and we're going to try to take as much as we can from him. It's been easier because he knows the place. It's been great to work under him," he added.
Manchester United next host Leeds in a league game on April 13.