The Italian lambasted his men for not matching the spirit of the veteran striker, after the San Siro side crashed to an opening day defeat
Summer signing Andrea Poli gave the Rossoneri an early lead, but it was Toni's brace on his debut for the promoted outfit which saw the hosts fightback to clinch victory.
And Allegri made no effort to conceal his anger at a spineless performance from his side.
"We were only a team for 13 minutes," he told reporters after the game.
"We revived Verona, who had been struggling. Toni set the example and fought like a lion, which ought to have been our spirit. We must play with more hunger to bring home the results.
"I am more angry than worried, we made mistakes technically and exposed ourselves to their counter-attacks. Once ahead we had to do things differently and we didn't.
"In order to get our results, we need a different mentality. Verona deserved the victory, so this should make us reflect."
With Milan's vital Champions League play-off return leg against PSV Eindhoven on the horizon, the 46-year-old fears their domestic defeat could have a knock-on effect in Europe.
"Losing like this is painful as it's the first week, especially as we have the important Champions League game against PSV on Wednesday.
"Some players have not managed to do much training but that cannot be an excuse. The market? We'll think of Wednesday, and then we'll see."
Milan drew 1-1 with Phillip Cocu's side last week in the first leg of their Champions League play-off clash as they bid to make it to the group stages of the competition.