Bath's hopes of snatching a place in the Champions Cup quarter-finals fell short in Italy as they failed to win by as many points as they needed to overtake Saracens.
They then discovered that Toulon had picked up a losing bonus point at Llanelli, confirming their fate.
Todd Blackadder at least had seven tries to savour in a 47-28 away victory, but the fact they failed to get a try bonus in their home clash with the Guinness PRO14 club probably did for them in the end.
It did not help either that they conceded four tries in Treviso.
On a day when the visitors needed to get off to a flying start in their pursuit of points, they found themselves falling behind to a 13th-minute try from Luca Sperandio as he faithfully followed up a chip into the Bath 22 and profited from a howler by Freddie Burns as he gave up the ball.
That score prompted an immediate reaction from the Bath forwards as they turned to their driving line-out to bag a try from hooker Tom Dunn and a penalty try.
Three more tries flowed before the break as Matt Banahan, Anthony Watson and Jonathan Joseph fired the visitors into a 35-7 lead.
That left them chasing 20 further points to catch Saracens, while still hoping Toulon could beat the Scarlets and stop them from getting a bonus point.
That would not happen, though, and neither was the 20-point chase accomplished.
Instead, the home side won the second half 21-12 as they plundered three more tries to end their pool campaign on a high with a bonus point.
They hit Bath with two sucker punches at the start of the second half when Sebastian Negri drove over from close range and Tommaso Benvenuti raced in from halfway after picking up a loose ball and showing a clean pair of heels to the Bath defence.
Tommaso Allan converted them both and that cut the gap to a mere 14 points.
Bath had to go back to the strength of their pack and it was another driving line-out try from new England squad member Zach Mercer on the hour mark that got the momentum back.
The final Bath try came from the old campaigner Luke Charteris, his first for seven years, as he took a line-out ball and crashed over, but there was a sting in the tail for the visitors as Monty Ioane sped over in the right corner for the bonus-point try.
As if that was not bad enough, Allan added the touchline conversion just as news of the Scarlets 30-27 win over Toulon came through.