The league leaders got back to winning ways on Sunday with a 2-0 win over Palermo, quickly putting a 1-1 draw with Sassuolo behind them.
Allegri knows Juve, who had a perfect record in the league prior to being held with Sassuolo, cannot afford to switch off as they seek to retain top spot.
"We dropped two points against Sassuolo, and this proves that games in this league aren't easy by any stretch of the imagination," Allegri told a media conference on Tuesday.
"I can't see Roma slipping up too often so we need to be at the races in order to maintain our stride."
Juve travel to Genoa on Wednesday, with Allegri concerned that the pitch at the Stadio Comunale Luigi Ferraris could hamper his side following recent floods.
"It will be very tough," he added. "Genoa have lost just once in the last seven games.
"They play attractive football, like to attack and show decent movement up front.
"I'm concerned by the state of the pitch, given the recent flooding in the region, and this makes it harder to put in a good display from a technical point of view."
Gianluigi Buffon is set to make his 500th official appearance for Juve in the match, but Andrea Barzagli, Martin Caceres, Patrice Evra and Simone Pepe remain absent.
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
‘He’ll still be playing at 40 at a good level because he’s in such good shape and looks after himself so well. He does everything to be a top professional’: Ex-Liverpool coach insists Mohamed Salah has plenty more miles in the tank
