The Blues named the mastermind of the Lions' AFL flag three-peat as their director of coaching under Josh Fraser, who was appointed full-time after a successful stint as interim boss last season.
The 65-year-old Fagan considered offers from multiple Victorian clubs after stepping down as Brisbane's coach following the Lions third consecutive premiership.
Alongside teammate Conor McKenna, McCluggage posed with Brisbane's three premiership cups on Melbourne Cup day at Flemington.
McCluggage, who gingerly held the 2026 cup aloft after some "off-season maintenance" on his shoulder, suggested the Blues had pulled off a major coup.
"We'll definitely really miss Fages but he was tired of the head coaching role," he told AAP on Tuesday outside TAB's birdcage marquee.
"It's a really stressful job and I'm really glad he's back with his family, but also able to keep himself busy because he's not someone that could just sit at home and completely stop.
"He loves his footy and he loves his development. So I think it will be great for Carlton and pretty jealous that they've got him."
McKenna, who recently signed a two-year contract extension, said it was a little weird to see his former Lions mentor in a Blues polo shirt.
"I suppose he was probably always going to work in football," the Irishman said.
"So probably a bit strange to see, but expected."
Brisbane's search to find a replacement for Fagan is entering its closing stages.
Lions midfield coach Cameron Bruce, former Collingwood coach Nathan Buckley, 2018 West Coach premiership coach Adam Simpson and Collingwood senior assistant Hayden Skipworth are the final four candidates.
Each was due to be interviewed by the Lions' selection panel before the end of the week.
McCluggage said the playing group expected to learn their coach for 2027 and beyond in the next week or two.
"I really like that they're going through a process," he said.
"Whoever gets the job will have earnt it."
While not throwing his weight behind any particular candidate, McCluggage backed Bruce to return to the fold if ultimately passed over for the senior job.
"He's a pretty selfless bloke and he loves the group," the Lions star said.
"So I have no doubt that he'd come back in and give his full effort again as a mids coach.
"He was doing so much of our tactical stuff as an assistant coach.
"He's so valuable as that and he'll be as a head coach if he happens to get the role as well."
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