Milan had the chance to make third place their own at the Stadio Artemio Franchi and goals from Riccardo Montolivo and Mathieu Flamini briefly opened a nine-point gap on Vincenzo Montella's Viola, who had Nenad Tomovic sent off between times.
But a clumsy final 30 minutes from the visitors saw Adem Ljajic and David Pizarro both score penalties to earn a 2-2 draw, before Mario Balotelli ruled himself out of next week's crucial meeting with Napoli by picking up a needless yellow card.
Allegri, however, is remaining positive and resolute in his mission to wrest second place from the Azzurri.
He told acmilan.com: "It's two points thrown away and we have to treat this as a lesson.
"Now we can look at the positive side as the team are doing well and four months ago no one would have imagined that we'd be six points ahead of fourth place.
"Football is strange. There are games that you should win and you don't and vice versa.
"They're all tough games but if we play with the right attention levels as we did in the first half then we can get third place or even second.
"But if we leave the field after the first 45 as we did today [Sunday], we could end up seventh or eighth."
Italy international Balotelli has scored seven goals since arriving at San Siro in January but, after failing to add to his tally in the last two games, he will now be unavailable to Allegri against Walter Mazzarri's Napoli next weekend.
"Balotelli took a lot of knocks in the first half and I can't rely on him to make the difference every week," Allegri added. "I'd like that, but it can't happen.
"He was bound to miss a match at some stage anyway. (Giampaolo) Pazzini is in good form though and we'll have to prepare well to face a team that are doing great things."
Montella, while regretting his side's fragility through the first 45 minutes, praised the steely mentality shown following the restart.
He told La Repubblica: "The mental strength of this team brought us back into the match.
"We still had the courage to attack them when we were two goals down midway through the second half.
"It was a great reaction and it's inspiring to see a group who believes so vehemently in what they're doing, against a strong team and a man down."