Hearts had to leave the stadium minutes after Saturday's drama-packed defeat, complaining there had been a "menacing and threatening" atmosphere inside the stadium as a pitch invasion immediately followed Celtic's late, late third goal on their home Parkhead turf.
"Heart of Midlothian utterly condemns the shameful scenes at Celtic Park this afternoon which have, once again, embarrassed Scottish football," a statement from the Edinburgh club said.
"Reports of serious physical and verbal abuse towards our players and staff, both on the pitch and elsewhere, are deeply disturbing. We are investigating this fully and are in dialogue with Police Scotland."
In an astonishing climax to the season, visiting Hearts, with their Australian midfielder Devlin playing a key role in midfield, had been closing in on a first title for 60 years as the sides were locked at 1-1, a draw being enough for the Edinburgh visitors to prevail.
But Daizen Maeda and Callum Osmand ended up scoring the late goals that earned Celtic their record 56th Scottish title and ensured the 41-year-old duopoly of Celtic and Rangers 'Old Firm' title domination continues.
When Osmand struck with virtually the last kick of stoppage time, chaos ensued with delirious Celtic fans streaming on to the pitch after a week in which the title race drama had dominated the national news in Scotland.
In a dramatic finale, Maeda scored from close range in the 87th minute but the offside flag went up.
Yet, just as in midweek when Celtic were rescued by VAR with the award of a late penalty that enabled them to beat Motherwell, an agonising wait finally ended with the goal being allowed to stand on review.
Hearts sent everyone forward in desperation for a final corner, but when it broke down with the Jambos' keeper Alexander Schwolow stranded, Osmand broke away to slot into an empty net.
It was the ultimate misery for Hearts, who could taste glory when captain Lawrence Shankland headed them in front from a corner in the 43rd minute.
But Celtic were level before halftime, again aided by VAR when Alexandros Kyziridis was judged to have blocked a cross with his arm and Arne Engels scored from the penalty spot.
It meant despair for the 27-year-old World Cup-bound Devlin, who's played a huge part in Hearts' breakthrough season and may have been playing his last match for them with his contract up. His family were all over from Australia to watch his big day.
But for 74-year-old Martin O'Neill, who'd guided Celtic to a fourth title after being persuaded out of retirement twice to manage the club again amid crises, there was nothing but joy.
"The players, the coaching staff have given me a reason to live - that's not to say my family haven't! - but this is the most special place on earth," he told his adoring supporters.
"When there is absolute unison in this stadium, it's a sight to behold. The players have been absolutely magnificent."
