The Reds came from behind to win 2-1 after Georginio Wijnaldum and Emre Can found the net to negate Ashley Barnes scoring the Clarets' first goal at Anfield since 1975.
It extended Burnley's woeful away record to 12 defeats and two draws on the road but helped Liverpool overcome their troubles against bottom-half sides, against whom all their five league losses have come this season.
"It is the first ugly game we won. We all have to get used to it a little bit. Usually when we are not at our best we have lost," said Klopp.
"You cannot plan an ugly game. It was not our best game. Not too much football today.
"In this kind of play Burnley may be the best team because they are used to everything, they fight for the first ball, have a really good formation for the second ball, run in behind for the third ball.
"If you don't score early against them, you need to fight.
"If we want to stay where we are, then we need to win football games and we can't make the choice and say, 'Yes or no we want to play this way'.
"We usually win good games, but the bad games and the average games we need to be challenging too. We were today."
Klopp was asked whether his side had the right mentality to compete against the 'lesser' sides, especially as their record against top-six rivals this season is unsurpassed.
The criticism has been that his players do not have the stomach for a fight.
"Mentality issue? No, it is a question of confidence," he added.
"We don't live in a dark corner and not know about the things people speak about us.
"It is deja vu. You try everything before the game and then you concede nearly in the first situation."