Amorim was sacked in January having been widely criticised in his time at the club due to a failing system and philosophy, along with strange calls like refusing to play star midfielder Kobbie Mainoo, who's thrived under Carrick having been drafted back into the team.
The Red Devils players in general have improved dramatically under the interim boss and now sit third in the Premier League; well placed to qualify for the Champions League for next season.
But Maguire enjoyed his time under Amorim and believes the Portuguese boss will go on to achieve great success elsewhere.
"I think Ruben was really good with me. I pretty much played every game under Ruben when I was fit," Maguire told The Mirror.
"I don't really have much bad to say about Ruben. I really like Ruben, I think he's got great ideas. The ideas just didn't work at Manchester United.
"I do believe he'll go on and have an amazing career, and his next club he'll probably go and win many, many football matches.
"It just didn't click or work and I think us as players have got to take a lot of responsibility for that as well.
"But I think he has led the club in a direction, and I do think he deserves a lot of credit for that, where he's built a good, solid squad and I do believe that he deserves credit for that.
"I spoke to him when he left. He wished us all the best. I'm sure he would have been upset, but I know he's still really, really young and I'm sure he's going to go on to great things in management."
United are now in the driving seat to secure a place in next season's Champions League following an impressive run of form under Michael Carrick.
And Maguire believes the former United midfielder should be under strong consideration from the club's hierarchy to extend his stay at Old Trafford.
"Listen, Carrick coming in, he's been amazing. He speaks really, really well. He's tactically very, very good," Maguire said.
"He's brought in some amazing staff. Steve Holland, amazing to bring his experience in and someone he can lean on.
"He's got Jonathan Woodgate and Jonny Evans there helping the younger defenders at the club and all the defenders giving us tips.
"Listen, it's not up to us. I think there's seven games left. We've put ourselves in a great position. I think we've got to finish the season strong, and I think he should go right into the mix of the other candidates and let the process begin.
"I'm sure it will do and I'm sure it's going to be a thorough process, and it's going to be a big summer. We know that for Manchester United. We need bodies in, bodies to help the squad. We know that. We need improvement in the squad. We need more bodies. It's going to be a big recruitment in the management department, and I'm sure that the hierarchy will get it right."
Casemiro says his impending departure from Manchester United will not be reconsidered, despite a strong late-season revival that has reignited calls from supporters for the veteran midfielder to stay.
Harry Maguire has confirmed he is in discussions with Manchester United over a new contract, with a decision on his future expected in the coming weeks.
Kobbie Mainoo has rapidly reasserted himself as a key figure under Michael Carrick, with the midfielder enjoying a notable resurgence that has silenced earlier doubts about his role and effectiveness.
Tottenham have paid tribute to interim head coach Igor Tudor after the death of his father - the reason behind his absence from post-match media duties following Sunday's 3-0 home defeat to Nottingham Forest.
