United focused heavily on strengthening their midfield after Casemiro's departure and a serious injury to Manuel Ugarte. Andrey Santos, Youri Tielemans and Carlos Baleba arrived for a combined fee of around 155 million pounds.
While some Premier League rivals spent heavily on individual signings, Carrick said United had to work within their own financial limits.
"We went into the window wanting to come out stronger from the group that we had last season. We've definitely added to that," Carrick told reporters ahead of Sunday's visit to Everton.
"I think we've done a lot of good work in that respect and the situation is what it is in terms of finances and what we can work with and what we're trying to get the most of.
"Certainly, the players that we've brought into the group I'm absolutely delighted with, and I think we've done some really good business there."
United remain particularly short at left-back, where injury-prone Luke Shaw is their only senior option.
However, Carrick insisted his players must be ready to adapt as the club continues its rebuild.
"What squad ever is the perfect squad? You've always got to find ways of adapting," he said.
"When you're building and trying to push to go through a period where we're trying to get to the top – that's the ultimate goal – you've got to make steps."
Joshua Zirkzee was also linked with a move away from Old Trafford, with Fiorentina and Juventus showing interest before Everton made a late approach.
The Netherlands international ultimately stayed at United despite struggling for regular playing time over the past two seasons.
Carrick believes Zirkzee can still play an important role.
"He wants to play more than he has done, and that's the good competition and healthy competition for places," Carrick said.
"Josh can do some really, really top things. I've seen it myself, and I know he can do that and looking forward to him doing that a little bit more often for us."
United began the season with a disappointing 2-0 defeat at newly promoted Hull but responded strongly by beating Ipswich 5-2, with Bruno Fernandes scoring a hat-trick.
Carrick will now look for another positive result when United face Everton at the Hill Dickinson Stadium on Sunday.
Matias Fernandez-Pardo is edging closer to a first start for Newcastle, although head coach Matthias Jaissle expects to wait until late before deciding if he'll face Leeds on Monday.
Mauricio Pochettino believes Tottenham should be awarded the 2016/17 Premier League title after Chelsea were punished for financial rule breaches linked to the Roman Abramovich era.
Liverpool goalkeeper Alisson Becker has been fined 8,000 pounds by the Football Association for kicking a substitution board after the Premier League draw with Nottingham Forest.
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.
