Eddie Howe's men defeated Liverpool in the competition's final at Wembley just over a week ago, with goals from Dan Burn and Alexander Isak proving crucial.
On Saturday past, Newcastle held an open top bus tour parade for winning the league cup.
Sensational scenes were sparked on Teesside as the fans gathered in their thousands.
Read more:
Speaking about the triumph and resultant celebrations on The Rest Is Football podcast, Shearer brought up the Celtic faithful: "We [Newcastle] just love our football, and we’ve been starved of success for so many years," he said.
"I think it was just a relief that we eventually got over the line. And yeah, we love our football.
"It’s a life. It is really, honestly. I don’t think I’ve been anywhere in the country where you have nanas and grandas, mums and dads, young kids and everyone who wears the black and white shirt like the Newcastle people do.
"And I think maybe in Liverpool or maybe in Glasgow for Rangers and Celtic, I don’t know, but it is very, very different and unique in Newcastle."
Newcastle hadn't won a trophy in 70 years before their success the weekend before last.
Boss Howe was heavily linked with the vacant Celtic job in the summer of 2021, although the Parkhead club eventually turned to Ange Postecoglou.