The AC Milan coach believes that avoiding defeat in facing Serie A's second-placed side is a strong return after his team's Champions League exploits against Ajax
Goals from Cristian Zapata and Sulley Muntari ensured that the Rossoneri twice came from behind to avoid defeat against the still-unbeaten visitors.
The draw moves Milan into the top half of the Serie A table and Allegri was happy with the result despite his side still sitting a massive 24 points behind leaders Juventus.
He said to Sky Italia: "In the end it is a good result. We used up so much physical and psychological energy on Wednesday for the Champions League game against Ajax and could have paid the price for that.
"It was an entertaining game for the fans - less so for us on the bench. We could have done more when the game was at 1-1 but made the wrong decisions at times and there were a few situations we should have avoided.
"But I think we played some good football in the second half and we did well against Roma's pressing. It was just bad control or a misplaced final pass costing us on a few occasions, especially when Mattia De Sciglio was finding space on the right."
Allegri was sent to the stands for his complaints after Riccardo Montolivo received a yellow card in the 73rd minute, a booking which means that the midfielder will miss the Milan derby against Inter on Sunday.
The coach remarked: "Montolivo was just talking to the referee - he is the captain. He did not touch the official so I don't see why he was booked. It is a shame because he will now be suspended.
"I would prefer to ignore the refereeing decisions. I accept them, I am sorry to have gone off the field and left my team even though it went well - we scored straight afterwards!"
Milan are now unbeaten in their last seven matches in all competitions, although five of those results have been draws.