"It can't be for the sake of it, but yeah, of course, we want to improve, we need to improve," Carrick said. "It's something that we're working towards, for sure."
The message came during a pre-season stop in Dublin, where United have been training at Carton House in County Kildare, with the United boss speaking after his side beat Leeds on penalties at Croke Park. It has been a summer in which top-four rivals Chelsea, Manchester City and Tottenham have all spent more than £100m, while even newly promoted Coventry and Ipswich have outspent United.
So far, only Youri Tielemans, Andrey Santos and back-up goalkeeper Karl Darlow have arrived to strengthen the first-team squad, with £8m Tottenham pick-up Tynan Thompson viewed as one for the future. Carrick was quick to praise the trio who have come in.
"I have to say, Karl, Andrey, and Youri, are exactly what we hoped, exactly what we expected in every way," he said. "Andrey, for such a young man to come in the way he's come in, his character, his personality is a dream. Literally, he's a dream."
But more business is wanted. United have made two failed approaches for Newcastle's Lewis Hall as they search for a left-back, and a central midfielder remains on the agenda too, with director of football Jason Wilcox in Ireland and in constant communication with his manager over targets.
"I think we've got a pretty good balance in all when you lay the squad out, but of course we would like more," Carrick said. "We would like more, we need to keep pushing for more. There's one or two areas where we'd like to improve and we feel that there's the possibility to improve, but again, that needs to be something that we can do that makes us better and improves the group, whether that's quality or whether that's a little bit of depth. That's something we've got to manage. That's pretty obvious."
Despite a frugal window so far, which has already seen United miss out on Elliot Anderson and Morgan Rogers among other targets, Carrick was reluctant to shy away from ambition for the season ahead.
"I think you've got to have the belief, you've got to be going into the season thinking we can achieve something special," he said. "Don't be going into a season thinking this could be a struggle. We've got to set out to really achieve something.
"We've definitely got the potential to achieve something really special. I'm not hiding from the fact, and we should aim to do that. I'm not going to make any crazy predictions, but I think on the back of what we've done, I keep saying it, I think that gives us the confidence to move forward. How quickly we keep moving forward, that's the challenge."
Marcus Rashford's situation remains one of the more delicate issues facing Carrick. The forward returned to the group on Sunday along with Kobbie Mainoo and Lisandro Martinez following extended breaks after the World Cup, and could feature for the first time in a United shirt since 2024, when he was frozen out by predecessor Ruben Amorim.
Barcelona passed up their option to sign the £325,000-a-week attacker permanently, and United remain open to moving him on as part of efforts to reduce the wage bill, having also chased a left winger all summer before missing out on Crysencio Summerville, who opted for a move to Saudi Arabia. Carrick stopped short of ruling out a sale before the deadline.
"He's a very good player, Marcus, and I think if you're going to have a career over 10 or 15 years, there's going to be times when things go in maybe a different direction," he said. "I think there's ups and downs, and that doesn't judge you as a one-off kind of judgment. It's what happens over time, and now we're in a positive place as a group, and Marcus can offer us so much. He has done (in the past), and he can do again, so in that respect, it's quite exciting."
Kobbie Mainoo's return has been more straightforward. Carrick kept in touch with the midfielder by text throughout the World Cup, in which he did not play a single minute, and is convinced he is ready to make an impact this season.
"The biggest thing for me, Kobbie's in a really good place," Carrick said. "I think he feels that. He's come back and he's come home and he's ready for a big season."
Manchester United return to the Champions League this term, meaning as many as 15 to 20 more fixtures than last season's historically low total of 40 games. Carrick is not underestimating the challenge that presents but believes his group is better equipped to handle it.
"We're not naive, we know what we're going into," he said. "But we feel we're a stronger group now than we were last season as well in many ways, so we've just got to capitalise on that."