Robertson confirmed on social media he had sustained “some ligament damage” but “nothing too major” in Monday’s 3-1 pre-season win over Osasuna.
The Reds had a wretched run with injury in their 2020-21 campaign, derailing their title defence with Virgil van Dijk and Joe Gomez among those to miss long periods.
Liverpool commence the new Premier League campaign on Saturday against newly promoted Norwich City.
“First off, my hope is that with the fit players it stays like this because the season starts and then you have different periods in the season and we need them all,” Klopp said.
“We need them all, that’s for sure. I am not famous for being negative, but I just hope it stays like this, that we can keep bringing people into the stadium and then you can see, both teams - yesterday and today - were absolutely inspired by that.
“It’s good for the people, it’s good for the players and it is much more excitement, much easier to enjoy everything, much more emotional.
“There is much more passion in and outside of the stands. Yes, I am very excited about the new season, absolutely.”
On Robertson, Klopp said he was hopeful the Scottish full-back could return in a month’s time.
“I think we got lucky with that. It could have been much worse,” the German said.
“We saw the footage, it didnt look too well. But I think we got lucky, it will not be too long. Im not sure [if] before the international break or after the international break, its difficult in these situations. But not too long.
“Obviously really good to have Kostas in the back hand, to have little Owen Beck in the back hand, which is nice as well.”