Juventus were hoping to re-establish a seven-point lead at the top of Serie A when they made the trip to Stadio Luigi Ferraris, but were handed a reality check after going down 3-0 inside half an hour.
Giovanni Simeone - son of Atletico Madrid coach Diego - scored twice early on, before an Alex Sandro own goal left Juve with a mountain to climb.
Miralem Pjanic pulled one back late on, but the match was already out of Juve's reach and Allegri was particularly irritated by his team's inability to get to grips with Genoa's physicality.
"There were 25 Genoa fouls and only eight from us," the Juve boss told Sky Sport Italia. "When those are the stats, it is impossible to win a game of football.
"We knew Genoa were tough and that we would have to play on their level physically, but the first half was really bad. The second was better, but by then it was too late.
"It's a setback. I presume it's because of a dip in concentration levels after qualifying for the Champions League [knockout phase].
"We conceded three goals from inside the six-yard box. Again, you're always going to lose a match if you do that.
"In every season there is a slip-up and this was ours, because we were just absent in the first 30 minutes. There are no excuses for that start.
"We were too lightweight. We still have a four-point advantage in the table, fortunately, but this match requires us to really sit down and think about things. It has to make us reflect and learn valuable lessons."