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."
Pazzini was hobbling on the sidelines after clashing with Daniele Portanova but three minutes later he opened the scoring.
The striker limped towards the edge of the area in the 22nd minute, a cross deflected into his path and he hammered the ball past Genoa keeper Sebastian Frey.
PAZZINI SWANSONG
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.
Bovo also hit the post with a thumping free-kick early in the second half before Balotelli gathered a through ball and rifled the ball home from a tight angle.
The game looked to be up for Genoa but after being chopped down by Bovo, the already-booked Constant gave his opponents a chance to get back in the game.
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.
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