"It's greedy if you like, but I want more," Carrick, who has made more Manchester United appearances than club luminaries David Beckham, Peter Schmeichel and Denis Law, told CNN Sport's Amanda Davies.
"You can't underestimate what that winning feeling gives to a player and gives to the squad."
"The trust level and respect level goes up between each other. You can't buy that experience."
It's been a long way back from the highs of the Alex Ferguson era, but three of English football's four domestic cups reside in the Old Trafford trophy cabinet.
First came the 2016 FA Cup, the departing Louis van Gaal's final farewell -- a watershed moment after three uncharacteristically barren campaigns and for Carrick "a big point" in the development of the squad.
In came Jose Mourinho -- a man Carrick describes as both "quite laid back" and "intense" -- quickly followed by the Community Shield, the annual curtain-raiser dismissed by some but appreciated by six-time winner Carrick, "because that's something you don't want to let go."
And then it was three, as the United players climbed the Wembley stairs once again, this time lifting the EFL Cup and breaking Liverpool's longstanding record to become English football's most successful club.
"Greedy again," Carrick smirks before turning his attention to the months to come.
'I still can't give up on it'
With just 12 Premier League games left to play, the Red Devils are 17 points behind leader Chelsea -- the two sides meet Monday in the FA Cup quarterfinals -- but Carrick is no mood to concede just yet.
When the Englishman insists the title race "can change so quickly," he speaks with the conviction of a man who has lifted the EPL trophy on five occasions -- more than any player from Chelsea or Arsenal in the history of the competition.
"At the moment this year looks a long way off, but in the back of my mind I still can't give up on it," the deep-lying midfielder tells CNN. "That's just me."
"Who knows? This year, maybe not. But if it's not this season, then next year this club has to be challenging for the title."
The 35-year-old isn't fussy about the shape of his silverware.
In the midst of a Europa League last-16 tie against FC Rostov -- this week's first leg in Russia ended 1-1 -- Carrick describes potential Champions League qualification via the continent's second-tier competition as an "added incentive" but once again insists it's all about that "winning feeling."
"There's no hiding from the fact that the Champions League is the place we all want to be, but we've got an opportunity in the Europa League," Carrick says. "We want to take that as well."
Carrick has often looked forward with his low, angled passing but affords himself a moment to look back at his finest moment in a United shirt: that wet night in Moscow nine years ago.
"I think the 2008 Champions League final was just a feeling I could never ever replicate, even if I won the Champions League again," he enthuses, having played all 120 minutes before calmly dispatching his shootout spotkick past Chelsea's Petr Cech.
"Everything that surrounded the game was just so intense; it was an unbelievable feeling."
Only one other member of that squad remains, but Carrick and club captain Wayne Rooney will be joined by the likes of Edwin van der Sar, Paul Scholes and Ryan Giggs for a "special" exhibition fixture to mark 11 years of service
Carrick admits he never envisaged he'd be at United for such a long time when he joined the club over a decade ago and hints he's matured since his $28 million switch from Tottenham in 2006.
But as measured off the pitch as he is on it -- his calming influence was compared by former teammate Gary Neville to a "piano" -- he hasn't always been celebrated in this way.
Less all-action, more dictation -- for so long the antithesis of England's favored central midfield pairing of Frank Lampard and Steven Gerrard -- Carrick has made just one international appearance at a major tournament among his 34 total caps.
A banner was displayed at Wembley last month during United's League Cup final win over Southampton comparing him to Scholes, but he refuses to bracket himself among the United greats, admitting it makes him "uncomfortable."
"I love playing for this club; I've become a supporter of this club," Carrick says. "It's something that I've lived for and lived through for the last 11 years."
His United contract expires at the end of this season, and he has been awarded a testimonial by the club.
"I've given everything. My whole life has been geared around playing for the club, as my wife will tell you," he adds.
"That's something I'm proud of. As for how good I am or not, I'll let other people decide."