Defeat means their future as a top-flight team was settled at the stadium at which it began with a convincing 3-0 victory in August 2017, and they join Derby in becoming only the second Premier League team to be relegated before the end of March.
Huddersfield boss Jan Siewert said, "I think we did very well in the first half. We encountered tactical situations very well and had offensive possibilities against a team which has the quality of Wilfried Zaha, for example. It was really great to see the lads fighting for each other.
"When you see this group on the pitch today, they made the home audience give them a round of applause after the game, even at half time we were impressed. It was great for us to see that we did so many things right."
A perfect summary of the season arrived as Palace eventually took the lead from the spot, a key theme of misfortune that has run adjacent to the Terriers' tough campaign.
"The penalty definitely summed up the season. We haven't had a penalty ourselves this season, but we've conceded eight to 10. The quality in the Premier League is so high that it completely takes the game in a different direction. But still, at 1-0 down, we fought and had a chance to equalise. The team on the pitch today made me really proud."