The Italian giants are going for a fourth straight league title despite the shock resignation of Antonio Conte in mid-July and replaced him with former AC Milan boss Allegri, much to the disappointment of many fans and pundits.
However, Pogba says the players are happy to be working with the 46-year-old, adding they are targeting another title victory.
"We still want to win the Scudetto," Pogba told reporters. "It's going to be harder this season because we won three times in a row and now other teams won't let us win again.
"So it's going to be even harder and you have to show everyone that we can win again, with another coach and that's it. I'm not scared, we can't be scared of any team, we are Juventus and we know what we can do."Allegri has already been successful, the team has great confidence in him, as well as the company and the president.
"We are happy to work with him. For the moment we are taking the same form as before, we're working a lot on ball possession. It's all very similar.
"When you play for three years with a pattern and you win, some things you shouldn't change much. You only need to maintain some features and improve others. And that's what the coach is trying to do."
The midfielder was then asked if he felt he will be able to score more regularly this season.
"A midfielder must defend, attack and create the game," he replied. "Scoring is a bonus and I will try to do it."