Alessandro Matri and Matias Silvestre scored the goals to peg the Giallloblu back to 2-2 after Marco Parolo and former Rossoneri striker Antonio Cassano had given Parma the first-half lead at the Stadio Ennio Tardini.
Milan might have even grabbed all three points with substitute Kaka pulling the strings, but it fell to Parolo to whip home a decisive free-kick four minutes into stoppage time, a 3-2 win taking Parma above their opponents and into eighth place.
The Rossoneri, who are 10th in the Serie A table and 11 points off the Champions League spots, have picked up only two points on the road this season.
Allegri was pleased with his side's spirited response, but is demanding more focus and composure through future games.
He told Milan Channel: "It was tough as Parma closed up well, but the players did well in the second half, the team reacted.
"It's disappointing to concede in the last 30 seconds of the first half and then in stoppage time in the second.
"We need balance and we have to start picking up points away from home an we've got very few so far.
"We have to improve and not concede not counter attacks. Games last 100 minutes and we need patience and calm to play all the balls in the right way and not to get caught in a hurry.
"Kaka is getting back into shape. We need all the players we have between the league, the Champions League and the Coppa Italia. They all have to fight for the team's cause."
With a modest haul of five goals, Parolo is now Parma's top marksman with his match-winning brace lifting the Ducale club into the top half of the table following a slow start.
"Yes, I scored the winner," he said, smiling. "But the real joy comes from just winning.
"We believed in the victory until the end and it was deserved.
"After we missed the chance to make it 3-0 we blacked out for 20 minutes, but we never fell apart.
"We still have less points than we deserve, but this was the best way to start a difficult week."
That week continues with Wednesday night's trip to Genoa, where Parma have failed to win since January 1994.