Egypt international Salah completed his move to the Reds from Roma on Thursday in a deal worth an initial €42 million , but which could go on to reach €50m with add-ons.
Asked if he returns to England a better player, Salah told Liverpool's website: "100 per cent, yes!
"Everything [has improved]. Even my personality was different, I was a kid – I was 20 or 21. Now I'm four years older, everything is different.
"I have lots of experience in three clubs: I was at Chelsea, then Fiorentina and then Roma. I have good experience.
"Yes, always [I have a point to prove]. Even if I see myself playing very well in one thing, I try to improve to do it better and better. I always think about the small details because I need to improve more and more.
"I was here [in England] and I have experience. I like to play here in the Premier League. I'm happy to be back and I'm excited."
Salah feels 2016-17, when he netted 19 times in all competitions, was his best season to date, but still has room to grow at the age of 25, having signed a long-term contract at Anfield.
"I think [it was my best], it was a top season," he said. "Nothing changed, the season before I also scored 15 goals.
"I am improving and doing better and better every year. This is why I'm in a new challenge and I'm happy to have this challenge. It is not easy, but I'm ready.
"I have played on the right. Last season with Roma we played five at the back and two strikers; I was a second striker, like a No.10. Sometimes I go on the left. I can play anywhere up front.
"I'm very happy to be here. I would like to win something with the club. Everyone knows the club is very big. We have to do something for the fans and win something."
Salah will wear the No.11 shirt at Anfield after the previous owner Roberto Firmino asked to become No. 9.