Domenico De Carlo's men went into the match second bottom in Serie A, with Juve tipped to claim a routine win and go nine points clear of Roma, who drew with Parma.
But the champions faltered at Stadio Dino Manuzzi, as Franco Brienza salvaged a deserved draw for the hosts 20 minutes from time.
Arturo Vidal missed the opportunity to give Juve a slender win when he put an 82nd-minute penalty wide of the target, but Allegri believes his team's attitude was the problem.
He told Sky Italia: "On the one hand such results are painful, but on the other they get our feet back on the ground to cancel out any signs of arrogance.
"Above all we need to reflect on our attitude in this game. It is a shame, as we would have extended our lead, but today proved for us and Roma that everyone must respect Serie A opponents, as games are won on the pitch, not on paper.
"We weren't in the right mood for this match. Cesena are in good shape, attack teams and on an artificial surface the ball moves quickly. If you are not reactive it becomes difficult.
"It was a bad performance. It is a pity because this would have been an important step towards the title. [But] our advantage remains unchanged."
