Allegri, whose side have taken only seven points from their first seven games and are 12 points adrift of Serie A leaders Juventus and Napoli, appeared to be clutching at straws as he faced the television cameras after the game.
"We played well, created chances but did not manage to score a goal," he told Sky Sports Italia. "We were just missing the result.
"We have to understand where we went wrong, once again we have conceded a goal from a set piece," he added.
Allegri was angry at a disallowed Riccardo Montolivo goal in the first half, said that Inter defender Juan Jesus could have been sent off before halftime and that Robinho should have won a penalty in the second half.
He also said that the free-kick from which Walter Samuel scored Inter's goal in the third minute should not have been given.
"The referee has heavily influenced the game," he added. "There was a technical mistake when he only added on 12 seconds at the end of the first half.
"There was maybe a penalty on Robinho, the red card for Yuto Nagatomo was obvious......and I have no idea what the referee whistled for on the Montolivo goal.
"The championship has not yet finished and I'm absolutely at ease."
Allegri overlooked the conduct of his own team who had five players booked and angrily protested every decision which went against them.
The low point was a tackle by midfielder Nigel de Jong who gratuitously followed up with his left knee after colliding with Walter Gargano, earning a yellow card.
Andrea Stramaccioni, who has won both meetings with Milan since taking over as Inter coach last March, did not want to get drawn into a discussion on the refereeing.
"I'd rather talk about football," he said. "The referee has officiated a difficult match, I lost my temper with the assistant but I have apologised.
"We never gave up when we were in numerical inferiority. I have seen the strong character of an important team."
- Riccardo Montolivo