Neil McCann says Celtic can be proud of the Scottish Premiership win - but know they should have achieved more.
The Hoops secured the title with seven games to spare following a thumping 5-1 victory at Partick Thistle on Wednesday and have lost just once - to Aberdeen - in the league this term.
Sky Sports pundit McCann saluted the panache with which Neil Lennon's charges have played this term, but says the Premiership success has been tempered slightly by failing to lift a cup and exiting the Champions League in the group phase.
"I don't think it will go down in memory as a classic win as it was always a certainty that they were going to be crowned champions," said the former Rangers winger, after the Bhoys seized their third title in a row.
"But they did it with a bit of style and had an immense League season, so they are perfectly entitled to celebrate it.
"I do think, though, they should have taken a cup with it - the fact they didn't was a big, big let-down - and maybe tried to make a bigger impact in Europe."
Celtic - who were beaten in the fifth round of the Scottish Cup by eventual champions Aberdeen and by Championship side Morton in the third round of the League Cup - bolstered their squad over the summer with players including Dutch centre-half Virgil van Dijk.
McCann says the 22-year-old ex-Groningen stopper will be vital for the Bhoys going forward - whether he stays at the club or not - while the onetime winger also lavished praised on January arrival Stefan Johansen.
"Celtic have brought a player of immense quality in Van Dijk, a guy who, for me, could play for one of the top four clubs in England, so if Celtic do sell him it will be for a huge price which they can then reinvest," said McCann.
"Plus, they now have Stefan Johansen, who I think will turn out to be a better player than Ledley, even though Ledley is a top player.
"He has a good range of passing in midfield and a real nasty steak about him where he digs in, while he also presses the game well and allows the players in front of him - Kris Commons, Anthony Stokes, and Leigh Griffiths - to express themselves.
"Add the fact he can get in the box and score goals himself and he is a quality addition."
Lennon's squad were unable to recreate their Championship League heroics of 2012-13 - when they beat Barcelona at home and reached the last 16 - this season, as they finished bottom of a pool featuring the Camp Nou side, AC Milan and Ajax.
And former Celtic midfielder John Collins believes the Glasgow outfit will continue to toil against the continent's big boys until they discover a forward capable of ripping the net regularly on the grandest stage.
But he is refusing to completely rule out Leigh Griffiths, snapped up from Wolves over the winter, becoming that man.
"Celtic have improved vastly from last year but they can't take that into Europe by spending £10-15million so they need to find cheap diamonds like they have in the past with Van Dijk and Gary Hooper," said Collins.
"They have struggled to find a top-class striker with pace who can score goals in the Champions League, and time will tell whether Griffiths, who is a pest, can come to the fore.
"But he will treat Champions League defenders with no respect. He will be in their faces and not stand off and admire them."