Liverpool's 68-game unbeaten home league run came to an end after Ashley Barnes netted a late penalty.
Reigning champions Liverpool have gone four league games without scoring and are winless in five, leaving them six points adrift of leaders Manchester United.
Klopp said it would be ridiculous to discuss the title race given his side's form.
"Look, how silly would that be if I sit here now, losing against Burnley, didn't score for the last three or four games – I don't know exactly – and now I talk about the title race? How silly would that be?" the Liverpool manager told a news conference.
"It's just we have to win football games – it was always like this. For this we have to score goals, there is no doubt about it. That's what we have to change and have to do better. If things don't work, you have to work harder, do the right things more often, longer and more consistent, all these kinds of things. "