Carrick has extended his present deal until 2015, with the option of an additional season.
It cements the 32-year-old's place as one of the most influential members of Moyes' squad.
And with skipper Nemanja Vidic also rumoured to be on the brink of a new deal, it is clear Moyes is keen to keep the bulk of his present squad, in addition to making the strengthening he feels is required.
"It's important we continue to improve the squad but it's also important you make sure you look after the ones you think you need to keep," he said.
"Everybody knew Michael's importance to the team and the club.
"It certainly wasn't anything he's shown me in the last few months (that influenced the new contract).
"It was just a matter of getting the contract signed and done and we're pleased we've done that."
Carrick has won five Premier League titles and a Champions League since his £18million arrival from Tottenham in 2006.
Yet he has been chronically underused at international level and despite returning to the England fold since Euro 2012, has still only won 31 caps.
"England have had some top midfielders over the years and Michael fits into that category as well," he said.
"He's been a great player for Manchester United and I think he is recognised by people throughout the country.
"They know what he can offer. I would be surprised if he wasn't part of the England squad that went to the World Cup."
Carrick will be missing when United travel to Cardiff on Sunday though after aggravating an Achilles injury in the win over Arsenal immediately prior to the international break.
With Phil Jones also sidelined and Marouane Fellaini still troubled by a wrist problem, it could mean an outing in central midfield for Ryan Giggs in the city of his birth.
Moyes did confirm skipper Vidic has returned to training after suffering concussion against the Gunners, although he will not be taking any risks with the Serbian.
"Concussion is something which you do need to rest," said Moyes.
"He's had his rest and when we bring him back hopefully he'll be fine.
"It is not a serious injury - concussion can be extremely serious - but he had a week off afterwards and we've given him a chance to recover.
"We've picked him up slowly from there."
United's win over Arsenal moved them back within five points of the Gunners at the top of the table.
And with Liverpool and Everton facing each other this weekend, plus Manchester City hosting Tottenham on Sunday, they have a chance to force themselves right back into the championship picture with a win on their first visit to the Cardiff City Stadium.
"I never thought we were out of it," said Moyes, when asked whether he thought his side were back in the title race.
"We just go about our job and try and win each game.
"Everybody knew at the start what it was going to be like.
"We knew we had a change of manager and there were always going to be problems, no matter what - whether it be winning games or different personnel in the team.
"I have said many times that Manchester United have proved over the years they improve as they go on.
"My history at Everton was as a slow-starter as well.
"Hopefully we're beginning to find our feet and we'll continue to improve."