The beleaguered Rossoneri boss has lamented his club's misfortune, claiming the team has not been getting the results its performances deserve.
The Rossoneri were trailing by a three-goal margin by the 50th minute, with subsequent goals from Nigel de Jong and Stephan El Shaarawy unable to spark a successful fightback at the Olimpico in Rome.
"Tonight, the team did create chances and worked hard," Allegri said to reporters after the match. "We've got to start winning games however, or we risk being embroiled in the relegation zone.
"We paid the price for Lazio's only chances in the first half unfortunately, and must learn to avoid errors, even if there were good points to take from this game.
"Recently, the team has not been getting the results it deserves. A coach will always be under examination, but we must keep working hard to climb back up the table."
The loss to Inter during the Milan derby and the latest capitulation to Vladimir Petkovic's men mean that Allegri has overseen the club's worst start to a league campaign in over 70 years.
Despite hovering just two points outside the bottom three in Serie A, the Milan board has, so far, continuously stood by their coach, maintaining that he has its full support.
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