A 4-1 defeat to Manchester City over the weekend has left the Reds in eighth position on the Premier League table, eight points adrift the Champions League places.
Last season Klopp's side made the final of three cup competitions, winning two, and finished runners up to Manchester City in the Premier League.
Liverpool have won every major club honour since Klopp took charge in October 2015.
Two Premier League managers lost their jobs over the weekend, with Leicester City sacking Brendan Rodgers and Chelsea dispensing with the services of Graham Potter.
"If it was my first season it would be slightly different," said the German ahead of Liverpool's game against Chelsea on Tuesday.
"I'm aware of the fact that I'm sitting here because of the past, not because of what we did this season."
"We have smart owners, they know about the situation," he added.
"There is no need [for me] to be afraid, I am here to deliver, I'm not here as a talisman or for murals on house walls.
"I know I'm still here because of what happened in the last few years.
"I don't like the fact that I pretty much have to rely on that. Is it right or not? We'll see in the future."
"I'm fully in, there's no doubt about that, but we have to sort it," he said. "We cannot continue playing like we do from time to time. That's not allowed.
"I'm really disappointed about us, that we do these kind of things, but it happened. Now we have to find a way out and that's what we're constantly working on."
