Man of the Match Anthony Stokes, who supplied the assists for Gary Hooper's brace and played a key part in Joe Ledley's late strike, felt the players comfortably handled the expectation of being favourites.
"It's just brilliant, we just wanted to finish the season on a high and to finish with the double has capped a great season for us," Stokes said on Sky Sports 2:
Midfielder Kris Commons believes the victory was just reward for the squad's efforts this season where apart from retaining the tile, Celtic reached the semi-finals of the League Cup and raised the profile of Scottish football by making the last 16 of the Champions League.
Commons said: "At the start of the season we wanted to win as many trophies as possible. Two out of three's not bad and the European campaign was magical."
That European run which included victories over Barcelona and Spartak Moscow raised manager Neil Lennon's stock considerably, with media rumours linking the Celtic boss with several jobs in England.
But Hoops skipper Scott Brown believes it is imperative the highly-rated Northern Irishman stays at Celtic Park.
"I think he's the main reason why everyone's here," Brown said. "We need to try to keep him and the players together."