Yohan Cabaye gave the Magpies the lead in the first half, but Mapou Yanga-Mbiwa was then sent off for a foul on Luis Suraez in the penalty area, and Steven Gerrard converted from the spot.
However, Paul Dummett restored the home side's lead, although Daniel Sturridge ensured that the match ended in a draw.
"I think we just about deserved a point. Liverpool are a great side and we matched them," FourFourTwo.com quotes him as saying.
"We then have to show another side, a resilience and character - and that got questioned about us last year - but we showed that is in the group and I'm immensely proud of the whole day."
The result means that Newcastle are now 10th in the Premier League.