The Eagles, seeking back-to-back wins in the Premier League for the first time since April 1, came unstuck late on as Mikel Merino found a way through at St James' Park.
Second-half sub Merino climbed highest for the game's decisive moment, leaving bottom-placed Palace with just three points and two goals to their name this season.
Hodgson was happy with his side's display on the whole, however, telling BBC Sport: "There were some very good performances from us in particular. The quality of our play was very good.
"We needed more than a goal to take one point and set plays are always a problem. It was unfortunate as our player got his head to the ball but headed it against the Newcastle bloke.
"I cannot criticise our performance. From the first minute to the last it was everything I expected and under normal circumstances would have got us a result."
Palace have now failed to score in their last seven away games in the Premier League - their worst such run in the top flight.