The manager said: “I congratulate them [Luton]. I thought they worked very hard for their victory.
“I think we can feel ourselves a little bit unlucky. We could have had some good moments in the game and certainly we asked some very tough questions of their goalkeeper [Thomas Kaminski], who had an outstanding game on the day.
“In that last 10 or 15 minutes, when we were pushing for an equaliser, I thought we were going to get that equaliser on at least three occasions, but it didn’t come, and I congratulate Luton for their valiant effort.
“They really did put an awful lot of work and effort into getting that victory, so we have to accept that we weren’t good enough to get the points we thought we could get from this game.”
On the returning Michael Olise, who scored Palace’s 600th Premier League goal with a superb strike to equalise in the second-half, Hodgson said: “We were all pleased with him. He’s one of the players in our team who can be pleased with his day’s work.
“Unfortunately, we didn’t have as many of those type of players as we’d have liked – who can say they were pleased with their day’s work – because with the players that we had on the field, I thought we should have been at least capable of coming away with at least one point, but unfortunately we threw that away after the equaliser. We allowed them back in for the winning goal.”
Hodgson also said that Palace were affected by injuries to key midfielders Ebere Eze and Cheick Doucouré in the early stages of the second-half.
He said: “They’re two of our more important players, of course, and it’s a devastating piece of news for us in a way, because Cheick’s injury is very serious.
“We don’t know quite how serious Eze’s is at this moment in time, but we were particularly frustrated because it was so unnecessary. Basically, what seemed to me, and maybe a lot of people watching the game, to be such an obvious free-kick, and then the player to land on him and restrain him like he did…
“For that just to be waved aside, not only did we not get the free-kick in a dangerous position, we also lost one of our most important players. That makes it an exceptionally bitter day for me.”