Juventus were forced to come from behind to claim a point against Real Madrid on Tuesday, Spain international Fernando Llorente's second-half striking ensuring a 2-2 draw.
Arturo Vidal had given Juve the lead from the penalty spot four minutes before the break, but goals from Cristiano Ronaldo and Gareth Bale turned things around for Real.
The Turin club now sit bottom of Group B on three points, one behind Galatasaray and Copenhagen after the Danish side claimed their first win of the competition by defeating the Turkish outfit 1-0.
But Pogba, who earned the penalty in the closing stages of the first half, believes teams should fear Antonio Conte's men.
"We put in a good performance, especially in the first half, and we did want to start strong," he told Sky Sport Italia.
"We were facing a great team and saw that the moment we make one mistake, they hit us with pace.
"We have to think about ourselves, focus on winning and only afterwards see what the other teams have done.
"Juve are Juve, so as a great team everyone should be afraid of facing us. We have to prove that we're strong and that we can win."
The Serie A champions host Copenhagen in three weeks' time, before travelling to Istanbul to face Galatasaray in their final group game on December 10.
