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.
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."
"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."
