Leicester are out of Europe despite four second-half tries giving them an easy Heineken Cup win over Aironi.
Two Naas Olivier penalties cancelled out a Billy Twelvetrees brace for Tigers, who needed other results to go their way if they were to progress.
Twelvetrees finally edged the hosts ahead and they added quick-fire tries from Thomas Waldrom and Ben Woods.
Geordan Murphy and George Ford also crossed but the Tigers finish third in Pool Four, behind Ulster and Clermont.
It has been a difficult season for the two-time European champions and their Heineken Cup challenge was effectively ended by their battering away to Ulster last weekend.
They needed Ulster to win away to Clermont to stand any chance of going through but the French side's 19-15 win in the Massif Central ensured the Tigers can now focus on domestic competition.
For the first 40 minutes they played like a side that knew their fate, and despite dominating possession they twice fell behind to the boot of Olivier.
It was only on the stroke of half-time that they finally went in front, courtesy of Twelvetrees' third penalty, but they were better after the break.
Captain Murphy scored a fine solo try as they eventually stretched clear before youngster Ford, the International Rugby Board junior world player of the year, shone in a late cameo appearance at fly-half.
He dummied his way over for the bonus point try and while he will go on to much greater things, Leicester's European dream is over for another year.
Leicester coach Richard Cockerill: "The game reflected the importance of it. We couldn't see Clermont losing without a bonus point so we knew there was very little hope of us progressing.
"We didn't get going and it was a pretty average performance.
"A number of our boys had a good run-out and nobody is injured but we tried to force the game too early and made too many errors in our passing."
Cockerill reported that Billy Twelvetrees will be leaving the club for Gloucester at the end of the season:
"On Monday he told me he was staying, on Wednesday I was told by his agent that he was signing for Gloucester, who have assured him of being first choice number 12 for them and his salary has been much improved.
"I did not want to lose him and he will be fully involved until the end of the season."
Leicester Tigers: G Murphy (capt); H Agulla, B Twelvetrees, A Allen, A Tuilagi; J Staunton, M Young; M Ayerza, G Chuter, M Castrogiovanni, E Slater, G Skivington, T Croft, B Woods, T Waldrom.
Replacements: Ford for Staunton (57), Harrison for Young (51), Stankovich for Ayerza (71), Stevens for Chuter (71), Cole for Castrogiovanni (51), Kitchener for Croft (71), Mafi for Waldrom (61).
Not Used: Hamilton.
Aironi: A Benettin; G Toniolatti , R Quartaroli, G Pizarro, G Venditti; N Olivier, T Tebaldi; A de Marchi, R Santamaria, F Staibano, Q Geldenhuys, M Bortolami (capt), M Bergamasco, S Favaro, J Sole.
Replacements: Bronzini for Tebaldi (66), Romano for Sole (62).
Not Used: D'Apice, Perugini, Del Fava, Ferrarini, G. Pavan, Pratichetti.
Ref: Jerome Garces (France).