Goals from Matheus Cunha, Bruno Fernandes, Benjamin Sesko and Lisandro Martinez saw off the Azerbaijani side at Old Trafford, in United's first Champions League fixture in almost three years. Carrick insisted the scoreline flattered his side somewhat, but said he was encouraged by patterns of play emerging through midfield that he has been working to implement.
"It's a good night for us, for many reasons. I think individuals were really good and, collectively, as a squad, with players coming onto the pitch who didn't start the game, doing ever so well in keeping the consistency in performance as a team," Carrick told MUTV and TNT Sports.
"The clean sheet is a big one for us. We are looking exciting and could have scored more."
The United boss was quick to praise the visitors despite the one-sided finish.
"If you look at the scoreline from the outside, maybe it looks like one of those nights, but I have to give credit to Sabah," he said. "As a team, they were difficult to play against and some of the quality of their football made us work for it, at times."
Asked what pleased him most, Carrick pointed to the balance between attack and defence.
"Some of our attacking play was fantastic, some of the football we played was really good. We were dangerous on the transition and defended, for the most part, really well," he said, adding that United "built on the signs we've already shown tonight" after a mixed start to the season results-wise.
On Manchester United's variety in front of goal, with four different scorers on the night, Carrick added: "Licha getting his goal is fantastic. There was a mixture of styles and type of goals but we'll take them, however they come."
He also pointed to improved understanding between his midfielders as a source of the team's progress.
"It's the little bit on connections, combinations and taking the ball and playing close together, at times," Carrick said. "I think that's something we've done a bit more this season, maybe we didn't have it as much in games last season."
United will look to carry that momentum into Sunday's Manchester derby against City.
"The confidence is there," Carrick said. "The way we played at Everton, the confidence was there for large spells, it just took a bit of a hit at the end. It's always nice to win at home and it's another big one on Sunday."