Rodrigo Palacio scored the only goal of the game four minutes from time at a sold-out San Siro on Sunday to heap more misery on Milan.
Allegri has only mastermind four Serie A victories this season and his struggling side are only five points above the relegation zone in 13th place.
Reports in Italy this week claim club legend Clarence Seedorf is being lined up to replace Allegri next season, but the former Cagliari coach is not fearing for his job.
He told Sky Sport Italia: "I work calmly, have important objectives to target and it's true we are behind in Serie A, but I trust in 2014 it will be different.
"We're in the (UEFA) Champions League and Coppa Italia."
Mario Balotelli spurned several chances on a miserable night for Milan and Allegri's frustration was evident after the game.
"The team was a little tired at the end, but unfortunately I had few options," he added.
"Riccardo Saponara played well while his legs lasted and Milan played well, but then we paid the price for one incident and I didn't have time to put Philippe Mexes on and cover their wings.
"I think it was a strong performance for an hour, then we should've defended better and Rodrigo Palacio scored a great goal.
"The derby is separate from the rest of the season. What disappoints me is that we concede many more fouls and get many more cards than our opponents. Something has to be wrong, because we get so many bookings.
"I'm angry at what I saw here.
"In the first six months, Milan have rarely been able to count on the same XI players, as we had numerous injuries and are the only Italian team left in the Champions League.
"It's a shame to lose the derby, but we have many more games to make up for it."
