Klopp’s men must avoid defeat away to Salzburg on December 10 to secure their passage into the knockout stages.
Dries Mertens threatened to inflict Liverpool’s first home defeat in the Champions or Premier League since April 2017 with a sweetly struck opener midway through the first half.
Dejan Lovren’s header protected that proud unbeaten run, but after a host of late winners in the Premier League this season there was no such joy for the hosts this time round.
“Our way was always the hard one,” said Klopp.
“We have to go to Salzburg. If we had done it (qualified) tonight we would’ve tried to win there and we will do the same now.”
Napoli remain a point behind Liverpool, but are well-placed to reach the knockout stages as they host winless Genk in two weeks’ time.
“It’s not easy to get a draw here. We suffered under pressure and began to defend too deep, but there’s no other way to emerge alive from Anfield,” said Napoli coach Carlo Ancelotti.
The Italians had travelled to Merseyside in disarray with Ancelotti seemingly on the brink of being sacked after a slump in Serie A.
President Aurelio De Laurentiis has also threatened to sell the entire squad and take legal action against the players after they refused his orders to be confined to a week-long training camp earlier this month.
However, the Italians are the only side to have beaten the European champions this season and proved a thorn in Liverpool’s side again.
“This is a healthy club within the locker room and with the desire of everyone to emerge from this difficult moment,” added Ancelotti.
“I spoke to the president, he was very happy with everyone and congratulated us all on the performance.”
Liverpool were unsettled by the early loss of Fabinho to an ankle injury and Klopp is worried that the Brazilian could be sidelined for some time.
“The biggest thing tonight is the Fabinho injury,” added Klopp. “That’s massive, it’s still early and we hope it is not too serious but it is pretty painful.”
The home side were still regrouping when the visitors opened the scoring on 21 minutes.
Mertens leaned into Virgil van Dijk as the Dutchman headed clear and was left on the ground holding his side.
Napoli played on and when the ball was played forward again Mertens was unmarked to run through before beating Alisson Becker from a narrow angle.
After a VAR review for a potential foul and offside, the goal was allowed to stand and there were a few more nervy moments for the home fans before Van Dijk got back to his feet and was able to continue.
Klopp grew increasingly frustrated on the touchline as Liverpool failed to find their rhythm before the break.
However, a talking to from the German inspired a second half turnaround.
Kalidou Koulibaly bailed out his goalkeeper with a clearance off the line from Roberto Firmino after Alex Meret dropped a simple cross into the box.
It seemed a matter of time before the equaliser arrived, but when it did it came from an unlikely source as Lovren rose above Mertens to power home James Milner’s corner.
Again a VAR check was needed as Mertens this time claimed to be the victim of a push, but the goal stood to leave both sides needing a point to progress on matchday six.
