Juve claimed a third successive title last season with Antonio Conte at the helm, only for the 45-year-old to leave the club and subsequently become Italy head coach.
Allegri's appointment as Conte's replacement was greeted with a mixed response, but Pogba believes they are even better this season under the former Milan boss.
A change in formation has seen Allegri use four at the back with more emphasis on the midfielders supporting the front men, and the France international is enjoying the new approach.
"Compared to last year we are stronger, there is more quality, the team is better overall," he told the Gazzetta dello Sport.
"Now we play much closer to the goal, it is much better for me.
"We attack with more men and we also counter-attack. We midfielders play behind the forwards, and it is also helpful for the guys up front."
Pogba scored twice in Juve's 3-0 win over Lazio on Saturday as Allegri's side maintained their three-point lead at the summit.