Goals from Cristian Zapata and Sulley Muntari twice brought Milan level at San Siro, but they had to settle for a point after Mario Balotelli missed two late chances to snatch the win.
Allegri admitted his side had struggled to cope with second-placed Roma in the opening exchanges, but was pleased with their fighting spirit.
"It was an entertaining game for the spectators, a little less for us," he told Sky Sport Italia. "We knew Roma were strong in space, but there were incidents we should’ve avoided.
"In the end it’s a good result, as we used up so much physical and psychological energy on Wednesday for the Champions League and could’ve paid for that.
"We could’ve done more when at 1-1, but made the wrong decisions on passes between the lines."
The draw sees Milan sit 10th in the Serie A table, 19 points behind Roma and 24 adrift of leaders Juventus.
