In an interview with ESPN, Pallotta said Salah's exceptional numbers were a revelation.
"The reason is probably because we utilised him differently than Liverpool have. They figured out the best way to utilise him," Pallotta said.
"At the time, we had him as a winger and you got (Edin) Dzeko in the middle and Dzeko's scoring 36 goals himself last year, so it's not like we didn't have someone in there tearing up the league last year.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
"Where I'm surprised, is how great he (Salah) is finishing... now you get the ball near his feet and it just seems like he's figured a way to put it in the net."
Liverpool reportedly paid 34 million euros (29.77 million pounds) to sign Salah, who returned to England two and a half years after leaving Chelsea following an unproductive 12-month spell in London.
Pallotta said the deal for the Egypt international, who was named Player of the Year by England's Professional Footballers' Association, was a bargain for Liverpool.
"When you look at it now, you can say it's an unbelievable bargain," Pallotta said. "The issue at the time was that when (director of football) Monchi came in, Salah wanted to leave, he had a year left on his contract so in another year you'd get nothing.
"He wanted to go back (to the Premier League) and prove himself, which he certainly has done."
(Reporting by Shrivathsa Sridhar in Bengaluru, editing by Ed Osmond)
