Per BBC Sport's Tom Rostance, the German said:
"I am disappointed, frustrated, whatever you want. We scored a wonderful goal and created wonderful chances. We shot the ball over the goal even when it was empty.
"We created five or six outstanding, big chances. Usually we score with one of them. I didn't see one more chance for Newcastle.
"They got one chance and scored. That doesn't feel too fair."
According to Sky Sports, Klopp added:
"I think the opponent made a lot more mistakes that were forced by us and did not get punished for it.
"At the end, the man of the match is from Newcastle and we have 80 per cent possession or whatever it was. That's the situation and that's how the world looks on it and we just have to carry on."
Klopp further discussed the fairness of the result in his post-match press conference, where has evidently unhappy:
B/R Football @brfootball
"Fair result" https://t.co/pO5Z6gKh9y2017-10-2 10:18:56
The Reds took the lead through a stunning effort from Philippe Coutinho but were quickly pegged back after Jonjo Shelvey slipped in Joselu with a lovely defence-splitting through ball, though the Newcastle man benefited from some good fortune as the ball deflected in off his shins from Joel Matip's recovery tackle.
Reds legend Jamie Carragher was unhappy with the team at both ends of the pitch:
Jamie Carragher @Carra23
Poor second half from Liverpool, again concede a poor goal & not clinical enough in front of goal. Then almost lose it from a set piece!!2017-10-1 18:17:19
Per Rostance, Liverpool had 68 per cent of possession and 17 shots but failed to find the net again as they mustered just two on target, including Coutinho's.
Mohamed Salah and Georginio Wijnaldum were guilty of missing clear-cut chances in the game, as was Daniel Sturridge, despite his impressive record of five goals in four starts at St James' Park prior to the match.
Newcastle created relatively little but still troubled the Reds at the back—they managed five efforts on target and almost won it at the end when Mohamed Diame had a shot blocked following some poor marking from a corner.
FourFourTwo and Sky Sports' Kaveh Solhekol illustrated the Reds' defensive struggles:
FourFourTwo ⚽️ @FourFourTwo
A visual representation of the space between Liverpool's centre-backs for that equaliser: https://t.co/5ALUIUBcoZ2017-10-1 16:11:00
Kaveh Solhekol @SkyKaveh
Only two Premier League teams have conceded more goals than Liverpool this season - West Ham & Crystal Palace2017-10-1 19:12:05
The vulnerable Matip and Dejan Lovren offered a marked contrast with the Magpies' centre-back pairing, per Sky Sports' Keith Downie:
Keith Downie @SkySports_Keith
Watched Lascelles & Clark closely for 5 mins or so - every step they took was mirrored. Newcastle's back two so well drilled by Benitez.2017-10-1 18:01:25
Ultimately, despite the slice of fortune in the equaliser, Newcastle were worthy of their point as they put in an organised, disciplined and clinical display—qualities the Reds have often failed to show this year.
Liverpool have a great deal of attacking talent, but with their porous defence and without a ruthless goalscorer in the vein of their rivals—such as Harry Kane, Alvaro Morata, Romelu Lukaku or Sergio Aguero—matches like this will always be a possibility.
If they're to beat Manchester United in their next match on October 14, they will need to improve significantly at both ends.