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Klopp and Salah together won the Premier League, Champions League, the FA Cup, two League Cups, Uefa Super Cup and Fifa Club World Cup.
"He knows this was the perfect club for him and he was the perfect player for us," said Klopp.
"Mo and I had big dreams, but we didn't dare to dream that big. I'm not sure we can appreciate it to the right extent - that will happen soon now. I wish him the best of luck because he deserves it.
"The numbers he produced and the standards he set, some of them, if not all, will stay unmatched in this modern Premier League era, definitely, because it's ridiculous to do that, and to do it for one club more or less."
Klopp, 58, added Salah is "one of the best" professionals and people he has met.
He said: "We texted the other day and we had our arguments, but it was always for the right reasons. It's always fine, especially now looking back, it's more than fine. And we are both really happy about being part of that incredible journey."
Asked whether it was the right time for Liverpool and Salah to part ways, with the winger still having a year left on his contract, Klopp said it was a "fair deal".
"It's not about me to make that decision but I think it's right that there's an agreement," said the German.
"I really think the whole relationship was a fair deal. An exceptional player, exceptional numbers, and he earned some money, of course.
"And now he can go wherever he wants and the club will have to find and will find other players, and that's absolutely OK.
"After all these years there should be no bad sentiment at all and as far as I'm concerned I can't see any."
Klopp admitted Salah will be "irreplaceable" but urged his former side to "find a new way" to play.
Next season will be the first time since 2016 Liverpool start a campaign without Salah in their squad.
"Yes, this specific kind of player is irreplaceable. That's always how it is. There will be a void that somebody will fill," Klopp said.
"The numbers for a winger are ridiculous. For a striker they are pretty much unmatched. That's how it is. So, if it is impossible, why should you try?
"I'm not in the role to advise anyone. But just bring players in and play the kind of football which can be successful. That is pretty much everything. "
Liverpool Legends play Borussia Dortmund Legends in the annual LFC Foundation charity match at Anfield on Saturday, with Klopp part of the hosts' management team.
