Allegri slammed his team, claiming they "should never lose a game like this" after Genoa struck in the fourth minute of second-half stoppage time with Alessandro Matri teeing up Luca Antonini to secure victory for the home side.
But in an effort to put a positive stamp on the defeat, Allegri revealed his hope that Juventus would learn from the experience.
"The championship is still long and we have many games left. From this negative aspect of tonight we have got to try to take something positive," he said.
"What I'm thinking of is that tonight we learnt that in this sort of situations we have to avoid taking risks and make sure we don't allow any counter-attacks when we don't have defence."
The 47-year-old coach declared Juve's 3-2 comeback win over title-rivals Roma earlier this month would mean little by the end of the season if the three-time defending champions dropped points against sides like Genoa, who moved up to ninth in the standings.
Roma joined Juventus on 22 points at the top of the table after they defeated Cesena 2-0 on Wednesday.
"With 30 seconds to go we should never lose a game like this. We can't lose such a game because you do not win a championship winning a single game against a championship rival but by gaining points over the whole 38 games we play," Allegri said.
"At the end of the season what counts is to be one point ahead of all the other teams and when it happens like tonight you must at least leave the pitch with a draw. We tried everything to win the game but we have no points to show for it.
"I repeat, with 30 seconds to go it's unacceptable to concede a goal like we did. We had a three point lead at the top of table on Roma, we wasted this advantage."
Allegri also paid tribute to Genoa's goalkeeper Mattia Perin, who made five saves to deny Juve.
"We went very close to scoring, hitting the post and the bar on two occasions," he said.
"We tried to shoot for outside the box a bit too much and Genoa's goalkeeper was brilliant."
