The 36-year-old was deemed surplus to requirements by then Milan coach Massimiliano Allegri and was eventually snapped up by Juventus on a free transfer.
Pirlo proved Milan wrong by guiding Juventus to four consecutive Serie A titles, though, and Galliani has conceded he should have held on to the gifted playmaker.
"Letting Pirlo go was my biggest mistake ever," Galliani was quoted as saying by La Gazzetta dello Sport.
"It was an error I made, together with a number of other persons. But don't ask me who the others were."
Galliani was close to luring Jackson Martinez to Milan earlier this summer, but he has no regrets that the Colombia international joined Atletico Madrid in the end, with the Rossoneri eventually signing Carlos Bacca from Sevilla instead.
"We were really close to signing him, but then he chose for Atletico instead.
"But we are happy with his decision now because that allowed us to bring in Carlos Bacca: a great player."
The Milan supremo also had his say on the potential arrival of Zlatan Ibrahimovic and Alessio Romagnoli from Paris Saint-Germain and Roma, respectively.
"Ibrahimovic has a contract with PSG until June 2016. That's all I can say about it at the moment.
"With Romagnoli, it all depends on Roma. We have offered them €25 million. But if they don't want to sell, then we have to accept that."