United sacked previous coach Ruben Amorim in January after a turbulent 14-month spell at the helm that saw the United players struggle to get to grips with his tactics, and Maguire credited his successor Carrick with restoring the team's confidence and getting them back to winning ways.
"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," Maguire told Sky Sports after setting up Casemiro for the first goal against Brentford.
"Everyone's believed in it, and we've gathered together. We've got the confidence. We know that we can score goals from anywhere."
Third-placed United looked comfortable as they cruised to a win that moved them to 61 points in the standings, 11 ahead of sixth-placed Brighton with four games left to play and five teams qualifying for next season's Champions League.
United have won nine of their 13 games under Carrick, paving the way for a return to Europe's biggest club competition.
"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 fifty-fifty, but we always ended up on the back of a defeat," Maguire explained.
"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."
Check out the match stats from Man United's win against Brentford.