Cristiano Ronaldo became the first player to score 400 goals in Europe's top-five leagues but Juve were still held to a 1-1 draw at home to Genoa on Saturday.
Daniel Bessa cancelled out Ronaldo's 18th-minute opener with 23 minutes remaining in Turin, where Juve's winning start to the season came to an end.
Allegri struggled to accept the result post-match, telling reporters: "It was the first match after the international friendlies and we had won eight matches before that.
"Supposedly, we were kind of invincible but, in fact, when there were only 30 minutes to be played, we sort of abandoned the match.
"Of course, this was a match played after the break for the friendlies, Genoa were very strong physically but I cannot accept those kind of things when there are only 30 minutes left to play. That's not acceptable, but we'll have to sort these problems out."
United rallied to take a 2-1 lead in the second half before conceding a 96th-minute equaliser at Stamford Bridge in London.
Allegri added: "When we were going into the changing rooms I mentioned Manchester United and how they had managed the last five minutes of their match...well, we have not only mismanaged five minutes, but 30 minutes!"
Juve's draw saw their lead atop the table cut to four points by Carlo Ancelotti's Scudetto hopefuls Napoli on Saturday.