Despite finding his team 4-0 down with two goals conceded in each half, Allegri saw positive aspects of Milan's play, though he admitted that their defending left a lot to be desired.
“We definitely have to improve our defending from set plays, while we were too disorganised and hasty in attack," he told reporters.
"After the break we were trying to get back into the game and conceded another two goals against the run of play, while the Roma goalkeeper had to perform quite a few tough saves."
The 45-year-old coach offered credit to his opposition, who currently occupy the sixth spot in the Serie A table, only a single place above Milan.
“I think the Giallorossi are one of the best teams in Italy and I am amazed we are so close to them in the table,” Allegri modestly claimed.
The coach insisted his side has more work ahead and suggested the loss of several high-profile players during the summer has lead to increased and undue cynicism among fans and pundits.
"People think we go from the stars to the gutter in a millisecond," Allegri continued.
"Don’t forget we went into this game with four wins and a draw in six games. Of course we can do better and the club will certainly do something in the transfer window, but it’s not as if we were challenging for second place before this defeat.
"Sometimes games go against you and we contributed to the result, but at the end of the day I think Milan played a good game.
"Roma deserve credit for making the most of the space we left and we know how dangerous Zdenek Zeman’s teams can be in these situations."