After Joselu cancelled out Philippe Coutinho's opener, DeAndre Yedlin appeared to pull Dejan Lovren down with a handful of his shirt shortly before half-time.
The referee did not point to the spot and Klopp was unsure how the foul went unpunished, though he acknowledged Liverpool's profligacy - Georginio Wijnaldum hit the bar, while Lovren and Sadio Mane were also unable to convert opportunities - was partly to blame for their failure to win.
"We had a clear penalty. I don't know what he has to do – pull the shirt off him?" he told BBC Sport.
44 - Newcastle v Liverpool has never seen a goalless draw in the PL (44 meetings) – only Newcastle vs Tottenham has had more (45). Vibrant.— OptaJoe (@OptaJoe) October 1, 2017
"If you don't help yourself no one else will help you. It will be like this until we score. We play like this, it makes sense that we play like this, usually we score in situations like this. We have to accept this and carry on.
"I am disappointed, frustrated, whatever you want. Away at Newcastle for each team will be a difficult place to play.
"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 more chances for Newcastle. They got one chance and scored. That doesn't feel too fair."
Liverpool have now won just one of their last seven games in all competitions, with captain Jordan Henderson ruing their inability to make a superior performance count.
"It feels like we are saying same thing. We do so many good things but come away frustrated. It is a strange feeling. We created good chances to win the game and were comfortable but overall we are frustrated," said Henderson.
"We have to keep going, keep creating and they will turn into goals. Saying that, we did keep going. I feel once we get one they will all start going in."