Juve suffered a rare blip when they were held 0-0 at Udinese last weekend, but second-placed Roma drew for the fourth successive league match to keep the gap at the top of the table to seven points.
Head coach Allegri insists that Rudi Garcia's side remain a threat, though, and will not allow Juve's standards to drop.
"[Is the] Scudetto already won? No chance," he said ahead of Juve's clash with Milan on Saturday. "There's still a long way to go and Roma are firmly in the hunt.
"We need to stay focused, alert and work our socks off until the title race is mathematically over.
"We'll require great intensity from a technical standpoint if we want to come away with an important result [against Milan]."
In Milan, Allegri faces a team he coached for four years between 2010 and 2014, leading the club to the title in 2011.
However, Milan have struggled in recent seasons and the club lie eighth amid a disappointing campaign, some 10 points adrift of the UEFA Champions League places.
Allegri is expecting a tough match, though, and is confident that Milan can challenge for European football under the stewardship of rookie boss Filippo Inzaghi - whom he coached during his time at San Siro.
"Milan may have had a few problems in January but played well in December, beating Napoli and drawing with Roma," he added.
"Milan have moved well in the January transfer market, bringing in four decent international players.
"Milan won their last game and can get themselves into a position to fight for a European place.
"Inzaghi's got all the right characteristics to enjoy a successful managerial career."
Allegri confirmed that Martin Caceres is a doubt for the match at Juventus Stadium, while Stephan Lichtsteiner is suspended.
