Balotelli netted on the hour, after he had replaced the other scorer Giampaolo Pazzini in the first half, to give Milan the cushion they needed following the 65th-minute dismissal of utility player Kevin Constant for lashing out at Genoa defender Cesare Bovo.
"The sending-off meant we suffered a bit," coach Allegri told Sky Sport Italia.
"It's annoying. We are at a stage of the season where this sort of stuff shouldn't happen especially at a moment in the match when we were looking calm."
It was Pazzini's swansong and he gave way to Balotelli three minutes later.
"We'll have to evaluate his condition over the next couple of days," said Allegri of his striker's injury.
Genoa reacted well to going behind and could have been awarded two penalties when M'baye Niang appeared to handle in the 33rd minute and again six minutes later when he pushed Andreas Granqvist as the defender was challenging for a header.
"They were both penalties," said Genoa manager Davide Ballardini.
Milan's defence held firm though and they can now eye second place in the table and automatic qualification for next season's Champions League.
Allegri's team take a 2-0 lead into this season's Champions League last 16 second leg in Barcelona in midweek.
