Klopp's side impressed with an all-out attacking style of play last season to reach the Champions League final and finish fourth in the Premier League.
But their last trophy was the 2012 League Cup, while they have not won the league title since 1990.
German Klopp was appointed as manager in October 2015 and reached the Europa League and League Cup final in his first campaign, but were beaten in both finals by Sevilla and Manchester City respectively.
"Can I promise next season any silverware? Of course not," said Klopp. "How could I? We will fight for it. That is what we promised in all the years and we did it.
"We were always close. If people want to judge our journey so far as a success or not purely on whether you have won something, do it. I have no problem with that. That is how the world is.
"But did people enjoy the journey, saw the final and said 'that's football, it can be happy' then we have been successful.
"Then we are close together with the fans and the team. It feels different. People were really ready to fight together until the final thing."
Read also:‘There is no leadership in NDC‘– Bagbin