A comfortable 3-0 victory over Brentford secured a first league win since mid-December and closed the gap to 11 points with a match in hand.
Klopp concedes in any other year that sort of lead would be unassailable but in a campaign being stretched by Covid-19, injuries and match postponements, he believes there remains a glimmer of optimism.
“We don’t have to convince anyone outside to believe. If they want to believe they can believe,” said Klopp, whose trademark triple fist-pump to the Kop returned at the final whistle.
“If you are with us, you will enjoy the ride and we will go for everything. We are ready to go as much as we can.
“This is not the situation to talk about a title fight, it’s 11 points now with one game in hand.
“In a normal world nothing happens anymore but what is normal nowadays? We try to do our part, there is nothing else to do.”
Having been frustrated by the visitors for 44 minutes, midfielder Fabinho nodded home from a corner just before the interval for his third goal in a week to break the deadlock.
After a first Premier League clean sheet in five attempts the only cloud was a late injury to Oxlade-Chamberlain which may see Klopp’s attacking options limited further with Mohamed Salah and Sadio Mane still at the African Cup of Nations.
“He was really good. That is the shadow on the game,” added the Reds boss.
“We don’t know yet but he rolled his ankle and now we hope it is nothing serious.
“Unfortunately, that is the life of a footballer. No one did anything wrong, it just happened, it is nothing to do with Alex, it could have happened to anyone.
“We will get the further or final information earliest tomorrow. That is the case in these situations. Absolutely too early, I have no idea [on the seriousness].”
For Brentford boss Thomas Frank – whose side have now lost four of the last five in the league – the performance still had positives.
“I thought we played 60 very good minutes and maybe even better the first 45,” he said.
“We played unbelievably well structured and with good discipline, defended low very well, put the bodies on the line when needed, gave nothing away in open play.
“We conceded on a set-piece and that should never happen. If you want to get a good result against a world-class team then you can never concede on a set-piece. Unfortunately we did that.
“I said to Jurgen I would have loved to see what would have happened if it had been 0-0 at half-time. When they scored to make it 2-0 it was a done deal.”