Barca were courting the French midfielder along with a slew of European teams, but he opted to return to Manchester United for a world-record fee of £89million.
Pogba, who was released by United as a free agent in 2012, saw his profile rise after helping Juventus claim four straight Serie A titles.
"Barcelona pulled out of the race to sign Pogba for economic reasons," Braida told La Gazzetta dello Sport.
"There is no discussion about his qualities and I think he will assert himself at Manchester United, but there will be criticism each time he is not at his best. People will see the transfer fee and expect him to win games on his own and this is simply not possible.
"Some figures are upsetting. No one is worth that kind of money. When you get to a certain level, we are getting too detached from normal life. We are talking about an operation of €150 million if we include wages
"You never know how a player will react to being overpriced like that. Maybe it will not even influence him, but the pressure must be enormous."