The Rossoneri coach felt that his side gave as good as they got in Turin but that they ultimately paid the price for gifting their hosts too many chances as they lost 3-2
Sulley Muntari put the Rossoneri ahead inside the opening 20 seconds but the hosts levelled through Andrea Pirlo before surging clear in the second half with goals from Sebastian Giovinco and Giorgio Chiellini either side of Philippe Mexes.
Despite their numerica advantage, Milan kept battling right until the end and pulled a goal back through Muntari, again, but they were unable to salvage a point, with Allegri arguing that they had ultimately paid the price for an error-strewn display.
"It was a good performance, though we made a few mistakes and allowed Juventus too many chances," the Rossoneri boss told Sky Italia.
"Both sides did well but we made more errors than they did. On the first goal, we lost the ball in our own half and sparked a counter [and were] forced to give the free kick. It's normal between two quality sides that a mistake will be paid for.
"I'd say overall in terms of performance that the team allowed little to Juventus, although we should have closed down their long-range shooters earlier.
"It's a long season, there is time to recover and we will do everything possible to achieve that. We'll see before the Christmas break where we are."
Milan's defeat - their third of the season - leaves them 12th in Serie A, 13 points behind leaders Roma.