The combative Australian, who coached the Wallabies to the World Cup final at the same venue a decade ago, was frustrated to bow out with a defeat, and vented his irritation about the officiating of the showpiece fixture on Saturday.
Cheika declared the decision to send his Tigers prop Dan Cole to the sin bin as "embarrassing for the game" after a late Emeka Ilione try for Leicester proved not quite enough to drag them to a late victory.
Yet Ilione's score would have given Cheika's team the lead if not for the penalty that Finn Russell put over after Cole had been penalised over a collision with the Scottish star flyhalf.
England prop Cole, in his last game before retirement, was sent to the sin bin, leaving Cheika to fume over both that decision and the earlier card for a high tackle from Leicester captain Julian Montoya.
"I thought we got nothing back from the referee at all and we kept on coming back and turning up," lamented Cheika.
"We scored three tries to two, that tells you something. I'm super proud of the players.
"Two men in the bin - the second one for nothing, really. It is embarrassing for the game that someone goes off for that. I'm allowed to be angry, but I'm over it and happy to accept the result now and get on with the next thing."
It represented an anti-climactic farewell for not just Cheika and Cole, but also Ben Youngs, the highest capped Englishman in international history.
Cheika reckoned he had to hold his tongue in his post-match press conference too as he reflected on the performance of referee Karl Dickson.
"For me personally, if the game is sending players to the sin bin for that, or even penalising…what do I say mate?
"If I say something, I'll get myself in strife and take away from the other team. I just have to beat myself up inside and try and keep as much as I can inside.
"I've got my feelings on the referee's performance but I'll take that up with [head of refereeing] Paul Hull as one last final…banter, let's say."
Cheika, at 58, decided in January not to extend his stay at the club which he's helped rejuvenate in his one season in charge.
Next season, Geoff Parling, the former Leicester and England lock who's been a key assistant to Joe Schmidt with the Wallabies, will take the reins.
For winners Bath, it was the end of a 29-year wait for a Premiership title as they secured a famous treble following their Premiership Cup and European Challenge Cup wins.
Tries by Thomas du Toit and Max Ojomoh had given Bath a healthy lead in the second half, only for Leicester, seeking a record-extending 12th title, to hit back with tries by former Tongan NRL star Solomone Kata and Ilione to set up a nail-biting finale.
