United have spent around 85 million pounds on Andrey Santos and Youri Tielemans, while goalkeeper Karl Darlow joined on a free transfer from Leeds as cover for new No 1 Senne Lammens.
With his first full Premier League season approaching, Carrick believes United can still improve in midfield and at left-back.
"We're delighted with the players we've brought in, first and foremost," Carrick told Sky Sports News. "We've improved the group. We've improved the squad in different ways - balance, quality and the direction we want to go in.
"We always want to improve. We want more, we need more. We keep looking forward to how we can do that. So that never stops. We're conscious of that and we've got to keep pushing."
United's midfield options have been affected by Casemiro's departure and an injury to Manuel Ugarte that is expected to keep him out for much of the season. They have also been linked with Newcastle left-back Lewis Hall.
Carrick would not specify how many players United could sign, but said additions must improve the squad.
"There's one or two areas where we'd like to improve and we feel like there's the possibility to improve," he said. "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 it's a little bit of depth."
United's net spend is around 30 million pounds following player sales and a sell-on clause from Mason Greenwood's move to Fenerbahce. They have also stepped back from deals for Elliot Anderson and Matheus Fernandes after declining to match rival bids.
Carrick accepts United must operate within the financial realities of the market while competing with their rivals.
"Money's money, I get that," Carrick said. "It's still about the football, and that's where the competition lies.
"We feel like we've got to be pushing for everything that we're involved in, understanding a little bit, being realistic of what the recent history has looked like as well, and that's over a period of time, but then actually the confidence we've taken from the last few months, and what we kind of achieved in the league.
"So there's a lot that goes into that, but certainly the situation is what it is as well, whether that's finances or whatever. For now, we've got to make the most of it, but we've got to keep pushing, really, and push everything in every boundary that we can to be able to win again, basically.
