Celtic captain Scott Brown immediately set his sights on surpassing this season's achievements after clinching the double.
Brown lifted his second trophy in two weeks after the Clydesdale Bank Premier League champions beat Hibernian 3-0 in the William Hill Scottish Cup final at Hampden.
Having exceeded expectations in Europe by beating Barcelona on their way to the last 16 of the Champions League, there is little room for improvement in their achievements other than adding the Scottish Communities League Cup to their haul while repeating their form on the continent.
But Brown is determined to keep the team progressing following their impressive display at Hampden.
"It's huge, not just for me, for every single player and the management staff as well, for everyone at Celtic," he said.
"It's a great club and the support we get week in, week out has been fantastic, so it's something to give back to them.
"We've got a great squad and hopefully we can keep the players.
"That's what we are trying to do. We have had a great season this year but we need to try and better it next season.
"We have three qualifiers coming up and we are back in quite early.
"Hopefully the squad can stay together but that's not up to me."
Manager Neil Lennon's next challenge could be his attempts to persuade Gary Hooper to stay at Celtic Park.
The 25-year-old netted twice against Hibs in what could be his last game for the club. Celtic rejected several offers from Norwich for Hooper in January but the English striker has so far resisted attempts to extend his contract beyond the end of next season and the club may cash in this summer.
With midfielder Victor Wanyama and goalkeeper Fraser Forster also the subject of transfer speculation, to a lesser extent, Lennon will hope his squad remains intact for the first of a potential six Champions League qualifying games in mid-July.
Another player whose future is uncertain is Hooper's Hampden strike partner, Anthony Stokes.
The Irishman played a significant part in all three goals, his dangerous crosses with either foot twice setting up Hooper before a great piece of skill and pass allowed Mikael Lustig to cross for Joe Ledley to make it three.
The 24-year-old's contract is set to expire but he has been in talks with over a new deal and his Hampden display has reinforced his worth to the club.
"Stokesy works really hard and once he's running at defenders, nobody knows what he's going to do," Brown said.
"He's got goals in him and he creates chances as well, he showed what a top-class player he is."
Despite Hibs pushing forward for spells in the second half, Celtic were not troubled after Forster saved Eoin Doyle's header just before Hooper opened the scoring in the eighth minute.
"It was a great performance, by both teams," former Hibs midfielder Brown said. "We both tried to play football and the support for both teams was phenomenal as well.
"They had a great chance but we have got a world-class goalie and he managed to keep it out.
"Two minutes after that we went up the park, Stokesy has crossed it and Gary has scored and it kind of killed their chances a bit. It pretty much kicked us on and settled our nerves as well.
"I think we started the second half quite poorly for the first five or 10 minutes but once again we got control of the game again, same as the first half, we managed to play our tempo and make them chase the ball a little bit more."
The game was also a personal high for Brown as he bossed the area in front of his back four after Hooper's goal blunted a lively start from the underdogs.
The Scotland midfielder played through the pain barrier for much of the campaign after being troubled by a hip problem and his season looked to be over at one stage after he underwent surgery on an abductor injury.
But the 27-year-old returned from a three-month lay-off to play the final two SPL games and was on top form at Hampden.
Brown joked to reporters: "I knew I was going to make it - I just didn't tell any of you.
"It was a great occasion yet again and for me to play 80 minutes, it helps me and helps my legs for next season."
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