Jose Mauri's strike on the hour mark was enough for bottom club Parma to deal Juve their first league defeat in 164 days at the Stadio Ennio Tardini.
The Turin club remain 14 points clear at the top of the table, with closest challengers Roma and Lazio both playing on Sunday.
But that was cold comfort for Allegri, who told Sky Sport Italia: "We didn't do anything in the second half and deserved the defeat.
"Monaco [in the UEFA Champions League quarter-final first leg on Tuesday] are another matter. We underestimated an important match and didn't realise it could allow us to secure the Scudetto. This was a perfect opportunity to seal the deal.
"We kept a low tempo and I don't think we won a single challenge out there. That says it all.
"I hope this can give us a positive shake-up, but we shouldn't need that. It was the chance to stay 14 points clear of Roma and Lazio, but we weren't up to it.
"Parma played well, while we were slow and risked conceding on three or four counter-attacks. We didn't control the game at all, as even in the first half Parma were dangerous.
"This was the match we had to play with maturity. Even if we couldn't win it, then we certainly shouldn't have lost."
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