AC Milan picked up a 2-0 victory at the Luigi Ferraris with goals from Giampaolo Pazzini and Mario Balotelli, but the sending off meant they had to play almost half an hour with 10 men after Constant stuck his head into Cesare Bovo's face.
And although Milan carry a similar 2-0 scoreline with them to Camp Nou, Allegri was annoyed that the Rossoneri had to over exert themselves after the dismissal.
“I thought we could have closed the match without using too much energy, but the sending off complicated things and made us struggle at the end," he told Sky Sport.
"At this stage of the season we can’t afford such behaviour seeing as second place and the quarter-finals of the Champions League are on the line.
“Tuesday we will go to Barcelona to play against the best team in the world and we will need our energy. Genoa did very well and we struggled to close down [Daniel] Toszer who found life easy in the middle.”
Allegri added that he was pleased with the first-half performance and a win that maintains pressure on second-placed Napoli.
“We had very few difficulties in the first half and were defending in an orderly fashion, while they were more dangerous in the second half," he continued.
"The important thing was to win to give us a boost in the standings and to get back to winning on the road.
“We must defend the third spot and maybe look even higher up if Napoli concede points to us, even if it will not be easy.”
And with the second leg of the last-16 tie against the Blaugrana next week, the Rossoneri coach was optimistic over the fitness of a number of his players.
Allegri said: “Balotelli didn’t have 80 minutes in his legs but he fought and helped us. He must improve his conditioning, but he will do that with work on the field in the coming weeks.
“Today he came on because Pazzini was injured or else he would have played one half. He [Pazzini] and Mexes will be evaluated in the coming days as I took them off for precautionary reasons.”
Milan's win over the Grifone on Friday has put them two points behind Napoli, while Genoa are still five points clear of the drop zone.