Palace have now conceded the opening goal in 17 different Premier League games this season - no side has done so more often - and are just three points above the relegation zone.
Speaking to Sky Sports News after the match, Hodgson accepted that his side have to stop gifting opponents the first goal in matches.
"It's been the trademark of our season," he said. "It's not a trademark we want to have. We want to come out at the start of the game and play like we did in the second half for the whole 90 minutes.
"I don't know if it's the tension or whatever it is that sometimes puts the brakes on performances. I think a bit of a change of style in the second half helped us to come to terms better with the way Newcastle play. I think in the second half we asked them a lot more questions but it's one of those things.
"It's a point that doesn't help either side enormously. We would both agree that we would like to have won the game but we have to keep going and make certain that when we can't win, we can draw."
Palace, who have lost just once in their last 10 home Premier League games, return to action next weekend with a trip to Everton.