Arne Slot said Liverpool rose to the challenge posed by a step up in opposition after beating Chelsea 2-1 to move back top of the Premier League on Sunday.
The Reds had not faced any of the top nine in the table in their opening seven league games of the season to give Slot a gentle start to the demanding task of succeeding Jurgen Klopp.
Liverpool did not have things all their own way at Anfield, but ground out another victory thanks to Mohamed Salah's penalty and Curtis Jones' second-half winner after Nicolas Jackson brought Chelsea level.
"The better the teams you face the more you need to fight," said Slot.
"It helps if you play against a Chelsea, it is a big game and everyone feels it. We felt it and the fans felt it because they were there for us today. We showed up, that was the most important thing."
The visit of a confident Chelsea side kicked off a daunting run for Slot's men in the coming months.
Liverpool face Arsenal, Brighton, Aston Villa and Manchester City in four of their next five Premier League games, as well as Champions League ties against RB Leipzig, Bayer Leverkusen and Real Madrid before the end of November.
"This is our biggest test, to play Champions League and Premier League, the hardest games, three days in a row," added Slot.
"Many other games were hard but this might have been the hardest maybe because of the amount of quality players they have and the structure they have. We had to fight really hard to get this one over the line."
Defeat for Chelsea was their first in the league since Enzo Maresca's debut as coach against Manchester City on the opening weekend of the campaign.
But there were plenty of positives for Maresca as the Blues were a different animal to the side that were thrashed 4-1 on their last visit to Anfield in January.
"We don't like to drop points and lose a game, but if you have to choose a way, this is the way," said Maresca.
"We came here and tried to control the game. For most of the game we played in their half and I thought the performance was fantastic.
"I came here many times in the past and I know how difficult it is but the way we controlled and managed the game was fantastic. This is the right direction."
AFP