The Egyptian has enjoyed a season to remember with 31 goals in 33 Premier League games.
He told ESPN: "He was sort of b****ing a little about, 'Did we overpay? I think we overpaid'.
"And I said, 'I'll buy you lunch'."
He said: "When you look at it now, you can say it's an unbelievable bargain.
"The issue at the time was that when [Roma 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 England after a spell with Chelsea] and prove himself, which he certainly has done.
"We can't tell you that anybody else was calling for Salah at anywhere near that kind of price, so there's a lot of teams that have missed out on the great play he's had this year."