Salah moved from Rome to Liverpool in the summer of 2017 for 42 million euros.
“Salah was an amazing boy, and I hated losing him,” Pallotta said on The Athletic.
The American businessman added: “I loved it. I did not want to sell it, but I had no other choice.”
He concluded: “Salah was sure to leave because he had what he wanted to prove. This is what happened.”
Salah, 28, played for Roma between 2015 and 2017 after moving to him from Chelsea for 15 million euros.
Salah scored 34 goals in 83 games he played with Roma before returning to the English Premier League from the Liverpool gateway.