He discussed the following subjects.
Palace's determination
"I thought that the best team won, I thought that in the first half we worked hard to keep our shape and keep them at bay but the fact is they had a lot of control. I think at times in trying to keep our shape, we were guilty of a bit of passivity on occasions.
"I didn't think there were a lot of chances in the first half but they certainly took theirs well. I thought we started the second half very brightly and the second goal was a real cold shower because the first five or six minutes we looked like we could do something here. It's a great credit to the players that despite the second goal they continued on the front foot as they tried to start the second half, and actually we got back into the game."
The killer goal
"When we scored the 2-1 goal, I thought that that was probably the result of some pressure that we were exerting and some control that we were establishing. But then with 20 minutes left to play, we made a few changes, we went if you like to try to get something from the game and as so often happens with teams of this quality, they find a way of picking you off and finishing you off with a third goal.
"That's what happens and that's what did happen. And we can only hold our hands up and admit that they deserve victory but we gave it our best shot especially in the second half."
United's physical prowess
"They've got three players who are six-foot, four-inches in their team. It's not that easy. It's not easy to stop Chris Smalling winning the first header and it's not that easy to stop Victor Lindelof winning the second header. You've got Pogba taking away one of your best markers as well and then of course the six-foot, three-inch Romelu Lukaku gets in on the action. They've got some good delivery and some very tall players."
Palace's draw with United in November
"The difference is today this was a much more even game in the sense of the possession and the way each team, when they had the ball, were able to mount some quite serious attacks. It was very much a counter-attacking job for us at Old Trafford and very much a question of defending extremely well and making certain they couldn't find a way through a very compact defence.
"So the two games are very, very different. There's no doubt that they are playing well, Manchester United. I thought tonight they did very well in areas of the game which aren't always that obvious to the naked eye. I thought their organisation was very good, I thought their work rate was extremely good. And of course, one of the things that we like to pride ourselves - our organisation and work rate - gets negated to some extent and then you're faced with the fact that they do have some very, very good players on top of that."
A disappointing outcome
"Sometimes those good players find a way to punish you as Lukaku did tonight. I'm disappointed, it would have been nice to have kept the good run going, it would have been nice to come away from this game with something but it would have taken an exceptional performance in some way or a little bit more fortune in some way.
"At the moment, the way United are going about their business and the way they approach this game tonight with the serious and the determination and the work rate, we were going to in some way have to find some goals or find a way of preventing goals which would always ask a lot of questions of us."
To watch Hodgson's press conference in full for free along with all the other post-match reaction, head over to Palace TV now. Or, if you're reading on the app, just click 'Palace TV'.