The 20-year-old left rivals Manchester United on a free transfer in 2012, joining Serie A champion Juventus where he scored five goals in his maiden campaign en route to the Scudetto.
And Vieira, who noted the similarities between himself and the Blues youngster, says he regrets City's failure to lure his "extraordinary" countryman to the Etihad Stadium.
"Many people say he is like I was. I think he is more offensive than me and perhaps better technically," Vieira told L'Equipe. "He is a player that I really like.
"I saw him play for Manchester United. That Manchester City did not take him when he left was a mistake because he is an extraordinary player."
Pogba was on the losing side as France suffered a 2-0 defeat to Ukraine in their World Cup play-off first leg and Vieira has urged the players to step up.
"In the French team, we have the players. These players must have a structure that allows them to grow," the former Arsenal midfielder continued.
"They must feel that the France team is as important, if not more important, than the club. This is not the case right now."