Cameron Carter-Vickers praised manager Brendan Rodgers for ensuring Celtic maintained the confidence and composure required to end a challenging campaign with double glory.
The Hoops looked to be losing their way as city rivals Rangers roared back midway through the league campaign to briefly overtake them at the top in February.
But Celtic found their stride when it mattered most and claimed 25 points from their closing nine matches to secure the league title before beating Gers in Saturday's Scottish Cup final.
"There was always that belief, and to be fair to the manager I think that's what he did well for us," said defender Carter-Vickers. "He kept us believing and kept a calmness in the group.
"We're a positive group and we knew that if we worked together and played for each other we'd get there in the end.
"I think we came to life towards the end of the season probably due to a combination of things. Whenever any club gets a new manager, it always takes a little bit of time for their ideas to settle into the group and stuff like that.
"Towards the end of the season I think you saw the fruits of what we were doing earlier in the season."
With Rodgers preparing for his second season at the helm since returning to the club last summer, Carter-Vickers hopes there will be further improvement at Celtic Park next season both domestically and in Europe.
"I hope so, that's our aim," he said. "We'll continue to work hard, and I'd like to think that will shine through.
"We always want to improve, not just in Europe but in the league as well. We know the Champions League is a very high level and we've got to prepare for that properly."
Celtic's end-of-season surge towards the double largely coincided with Rodgers having all his key players available after the likes of Reo Hatate, Callum McGregor, Daizen Maeda and Carter-Vickers endured periods sidelined by injury.
The centre-back was out for more than two months early in the season and then had further fitness issues in the first couple of months of this year before getting a regular run from March onwards.
"The beginning of the season was a bit frustrating for me because of the injuries but I managed to get fit and help the team towards the end of the season, which was good," said Carter-Vickers.