Leicester endured a frustrating start to their Heineken Cup campaign as they missed out on a bonus point in Italy.
Toby Flood landed two early penalties and converted tries from Tom Croft and Alesana Tuilagi to put Tigers 20-0 up.
Luciano Orquera got the hosts on the board with two penalties before the interval, and he added two more.
Tigers could only manage a third Flood penalty in the third quarter and a last-minute try for Niall Morris came too late to press for a fourth.
The failure to register a try bonus point may come back to haunt Leicester in what promises to be a fiercely contested group.
With powerful French outfit Clermont Auvergne and Irish province Ulster also in their pool, five points from both meetings with the Italian minnows appeared a minumum requirement for potential group winners at the outset.
The Tigers got off to a flying start at Stadio Brianteo in Monza and surged into a 13-0 lead within 15 minutes thanks to a pair of quick-fire penalties from Flood and a try from England flanker Croft.
With Sinoti Sinoti in the sin-bin, Leicester stretched the hosts either way and after working the overlap, Tuilagi released Croft to squeeze in for a converted try.
The big Samoan wing then took a short ball off Flood and crashed over for the second in the 25th minute, Flood converting for a 20-0 lead.
But Aironi hit back with two Orquera penalties, Flood missing one and landing another on the resumption.
But the Tigers could not build any momentum and Orquera landed a third, and then a fourth after 68 minutes following sustained pressure from the hosts.
Leicester should have grabbed a third try eight minutes from time when Tuilagi failed to hold onto Matt Smith's wild pass.
They continued to hammer away at the hosts but had to wait until the final minute for further reward.
Following some strong carrying by Thomas Waldrom, the visitors worked the overlap and captain Geordan Murphy threw a pinpoint pass to fellow Irishman Morris to score in the corner.
Aironi: R Trevisan; S Sinoti, A Masi, M Pratichetti, G Venditti; L Orquera, T Keats; S Perugini, F Ongaro, F Staibano, Q Geldenhuys, M Bortolami (capt), N Cattina, S Favaro, F Viljoen.
Replacements: G Pavan for Trevisan (62), Aguero for Perugini (46), Santamaria for Ongaro (64), Romano for Staibano (79), Sole for Favaro (40), Ferrarini for Viljoen (64). Not Used: Bronzini, Olivier.
Leicester: G Murphy (capt); N Morris, M Smith, A Forsyth, A Tuilagi; T Flood, S Harrison; M Ayerza, G Chuter, D Cole, L Deacon, G Parling, T Croft, J Salvi, T Waldrom.
Replacements: T Youngs for Chuter (52), Castrogiovanni for Cole (52). Not Used: Stankovich, Skivington, Mafi, Young, Staunton, Hamilton.
Referee: Neil Paterson (Scotland)