The Reds lead the table heading into the international break after moving two points clear of Manchester City, who have played one fewer fixture
After the in-form Sadio Mane had given Liverpool a half-time lead, Milner, Virgil Van Dijk and Alisson Becker combined to gift former Anfield forward Ryan Babel the chance to score Fulham’s equaliser.
But victory was ultimately secured in the 81st minute when Milner scored from the spot after Mane had been felled.
Speaking to Sam Matterface after the game, Klopp revealed the performance was a warning to their rivals that they have the fortitude required.
“The boys’ reaction was really good,” Klopp said. “They were really calm, I thought we were emotional.
After battering Bayern Munich in the champions League, returning to Premier League football was always going to be difficult.
And with Fulham fighting for their lives, it was an uncomfortable afternoon for the Reds at times.
But, with the international break looming, the German insists his team will focus on their own progress rather than title rivals Manchester City.