The France international returned to Old Trafford last summer after four seasons with Juventus, joining the Red Devils for €105 million plus €5 million in bonuses — making him the world's most expensive footballer.
Pogba went on to make 51 appearances in all competitions this past season as United won an EFL Cup and Europa League double.
While Pogba helped the Bianconeri claim four Serie A titles and two Coppa Italia crowns during his time with the club, Allegri had no hesitation to sell once he saw the massive number put forth by Jose Mourinho's side.
"I did nothing to keep Pogba," Allegri told Sky Italia. "Because when the club told me the numbers..."
After Pogba was a key figure for Juve's run to the 2014-15 Champions League final, Argentine playmaker Paulo Dybala served as the youthful catalyst behind the club's return to the showpiece event this year.
Asked to compare the two, Allegri said: "Dybala’s game is easier on the eye, but Pogba is extraordinary because he has physicality and technique."