The Italian says his former club could tell the midfielder was special straight away and were in "total disbelief" that the Frenchman had been allowed to leave Old Trafford
The France international moved to the Serie A side for just £800,000, spending four years in Italy before heading back to Manchester United this summer in a world-record £89.5m deal.
Pirlo says that while Juventus may have lost their prize asset they are still struggling to believe they managed to land him for such a nominal fee in the first place.
“On the first training session Pogba had with Juventus the players were laughing,” he told the Telegraph.
“We were not laughing for any other reason than we were just in total disbelief that this player with so much obvious ability was able to leave the club the size of Manchester United for free – and I think Juventus are still laughing.
“I will always remember that first day he trained at Juventus. He was only young but we could see he was special.”
Despite the massive transfer fee, Pirlo believes that Pogba will be a success at Old Trafford, particularly with Zlatan Ibrahimovic also now at the club.
“I think Pogba will make Manchester United a real force again. One player of that quality can change things,” he added.
"They will lift the players, the fans. You give any team Pogba and Zlatan in one window and they are capable of special things.”