The 25-year-old joined the Reds for a reported initial £34m fee from Roma, where he scored 19 goals and registered 12 assists last season.
Before joining Roma following a loan spell last year, Salah spent two years on Chelsea's books, but he made just 13 Premier League appearances.
Klopp, though, is not worried about the attacker's forgettable spell at Stamford Bridge, and he used Kevin De Bruyne as an example of why some players fail to perform at Chelsea.
"A lot of players have shown it is quite easy to struggle at Chelsea; De Bruyne is one," The Telegraph quotes Klopp as saying.
"The only thing that we really ignored was what he did at Chelsea. When he was at Basel [Borussia Dortmund] played them and we didn't know him. It was, 'What the fuck?'. It was unbelievable. The moment I said, 'Let's go for him', he was already at Chelsea.
"Then he struggled at Chelsea because it was too early. Then he went to Fiorentina and then Roma. The question is 'what did you not see in him?' because he played all inclusive football. He was quick, he played a lot of games, he created goals and chances and he scored by himself."
Salah and Dominic Solanke are the only players that Liverpool have bought in the summer transfer window so far.