The Rossoneri, who travel to Barcelona on Tuesday to defend a 2-0 first-leg lead in the last 16 of the Champions League, earned a 2-0 victory at the Stadio Luigi Ferraris thanks to goals from Giampaolo Pazzini and Mario Balotelli.
Despite the win, Allegri believes that Constant's dismissal on the hour could prove detrimental to his team's hopes of qualification at the Camp Nou.
"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 Italia.
"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."
Milan were knocked out by Barcelona in the quarter-finals of last year's competition.