Sunday's 3-1 victory over champions Manchester City made it 34 points from a possible 36 and established an eight-point gap over Leicester and Chelsea, with Pep Guardiola's fourth-placed side a further point behind.
In that run Liverpool have faced all their so-called 'big six' rivals, plus Leicester.
In contrast, City have played just the Reds and Tottenham.
"It's just the start, that's how it is, everybody knows that," Klopp told his club's website.
"If you would have told me that you can have 34 points (at this stage of the season), wow! It's pretty much impossible but we did it."
Klopp is now hoping his players return from international duty fit after forward Mohamed Salah and defender Andy Robertson withdrew from their respective matches with Egypt and Scotland due to ankle injuries.
Salah is understood to have aggravated a problem he initially sustained against Leicester last month, which kept him out of the game against Manchester United - the only league match in which the Merseysiders have dropped points - and already could be a doubt for the trip to Crystal Palace when the Premier League resumes.
Robertson has not trained properly for a fortnight but is hopeful a two-week break will allow him some much-needed recovery time.
It leaves Klopp sweating over the condition of the rest of his squad.
"Now the boys go for the last international break of the year. They have to come back healthy. You saw it how intense it was (against City)," he added.
"Hopefully they all come back healthy and then we go to Crystal Palace.
"I think the last games are somewhere on the planet on Tuesday in the week that we play on Saturday against Crystal Palace.
"So they will fly back on the Wednesday, Thursday have a recovery session and Friday, Saturday 'Hello, Crystal Palace'.
"That's the situation so nothing happens so far but it's still the best situation we could have asked for so let's hope we can carry on."