United begin their league phase campaign against Azerbaijani champions Sabah at Old Trafford on Thursday, returning to Europe's elite competition for the first time in three years.
Carrick, who guided United to third place in the Premier League during his interim spell last season before earning the permanent manager's job, is determined that his side will not simply enjoy being back among the best.
"It's a magical competition. It's where we all want to be," Carrick said.
"When you're out of it, you realise how special it is, and when you're in it, you want to make the most of it.
"We're delighted to be here, but we're not here to just enjoy the occasion. We're here to do business and go as far as we possibly can."
United have struggled in recent Champions League campaigns, exiting at the group stage in two of their last three appearances and failing to reach the last 16 since 2019.
Their early Premier League form has also been modest, with just four points collected from matches against Hull, Ipswich and Everton.
Carrick, however, believes United have shown they can raise their level against stronger opposition. They defeated Arsenal, Manchester City, Liverpool and Chelsea during the second half of last season.
"I think we're capable of doing some really good things in this competition and going further down the line in this competition," he said.
"Certainly not getting ahead of ourselves because some part of it is a new experience for some of the players.
"But the boys are used to playing European football for the most part in different competitions, and we'll take that forward, and we've got a squad that's strong enough to compete."
United played only 40 matches last season, their lowest total since the 1914/15 campaign, but their return to the Champions League will bring a much heavier workload.
Carrick also confirmed Matthijs de Ligt is nearing a return after almost a year out with a back injury.
Carrick believes his players must embrace the demands rather than see the schedule as a problem.
"We play Thursday, Sunday, Wednesday and it's what we're here for," he said. "It's about managing the group and having trust in everyone able to play."
Benjamin Sesko is in contention to make his first start of the season after scoring as a substitute in Sunday's 2-2 draw at Everton.
Morgan Rogers believes Xabi Alonso has made Chelsea an "exciting" team after the Blues continued their impressive start to the season with a 6-3 victory over Leeds in the League Cup on Wednesday.
Xabi Alonso has moved quickly to dismiss concerns over Levi Colwill's fitness after the Chelsea centre-back was withdrawn during the 6-3 Carabao Cup win over Leeds United.
Mikel Arteta praised captain Martin Odegaard following his excellent start to the 2026/27 season, urging his side to give him more of the ball during matches.
Andoni Iraola has eased concerns over Bradley Barcola and Milos Kerkez after both players were forced off during Liverpool's 2-1 Champions League victory over Atletico Madrid at Anfield on Wednesday.
