Bottom-placed Parma inflicted just a second league defeat of the season on Juve and ended a run of 20 unbeaten games.
Jose Mauri’s goal was enough for the Gialloblu to make it seven points from their last three games, and 16 for the season, while putting a minor dent in the Bianconeri’s hopes of a fourth-straight league title.
Allegri was disappointed with the result and told juventus.com: “It was an important game that would have enabled us to almost wrap up the league and maintain our exact points advantage over Roma and Lazio with eight games remaining.
“We got our approach all wrong. The absent players are no excuse. The fact remains that below-par displays don’t win games.
“We didn’t win a tackle out there and that tells you a great deal about the spirit Parma played with. They put in a decent performance, while we were slow and allowed them three or four breaks due to our errors in the second half.”
Juve’s lead at the top of the table could be cut to 11 points this weekend, although it was clear that their focus had already shifted to a more important midweek appointment, without taking anything away from a deserved victory for beleaguered Parma.
Juventus take on Ligue 1 side Monaco at the Juventus Stadium on Tuesday in the first leg of their Champions League quarter-final.
Allegri added: “We didn’t take the game to them. Our first-half performance was average and we did nothing after the break, deserving to lose.
“It will be a different game against Monaco, but today Parma was the most important match for us.”