Amorim, 41, was finally sacked in January with Man United tumbling down the Premier League table and out of both cup competitions.
Carrick has since come in on an interim basis, and the club are on the brink of qualifying for the Champions League for the first time since 2023-24.
Speaking to Sky Sports after their 2-1 win over Brentford, Maguire appeared to give his blessing on Carrick taking over on a permanent basis.
"I think obviously the results help that the feeling (of confidence about Michael Carrick) massively,” he said.
“We had two tough fixtures when Michael first come in, and I think everyone was probably looking at them thinking 'oh no', with Arsenal and Man City, and we managed to get the six points.
"Everyone's believed in it, and we've gathered together. We've got the confidence. We know that we can score goals from anywhere. I think we can still get a lot better at this formation as well. I think we can work as a back force, slide across the pitch a lot quicker, like we should have done.
"The results speak for themselves, since the manager has come in, and the formation has changed, we just seemed to pick up results. I think that the games previous, when Ruben was here, the games were 50/50, but we always ended up on the back of a defeat.
"Now it seems like it's the other way around, where we're a lot better in both boxes. We defend our box a lot better, and we're managing to be clinical in the other box."