The reigning champions surrendered their 100% start to the Serie A season after failing to build on Paul Pogba's 19th-minute equaliser against their winless opponents.
"I knew it would be a difficult game, particularly because our internationals only returned on Thursday, after having played two games," Allegri told Sky Sport Italia.
"Tonight, they put us in difficulty. We didn't play well technically and we had finished little in relation to what we created.
"The game remained open right until the end of the game. Their goalkeeper, Andrea Consigli, made decisive saves but we could, and should, have done more."
Simone Zaza opened the scoring for the hosts on a night when Allegri's side dropped their first points in seven games.