Palace even had the better chances on Saturday, but Hodgson insisted he was pleased to come away with a point.
"When we defended well enough to win the ball back and break out, we broke out good. I thought we had quite a few opportunities where I'm sure Jose on the other bench would have been a bit worried. I'm very proud of the team's performance," he told 'Sky Sports'.
"I thought it was a very even game, and it says a lot that towards the end that the same 11 players for us are dealing with Sanchez, Fellaini and Rashford, that sort of wealth of talent to bring on tells you where the two teams are.
"I've got to be extremely proud of the performance, by playing football and justifiably taking it to the opposition.
"I thought the team tactically were excellent throughout. We were concerned at the end about the crosses, with so many big games on the field, we aren't that big a team, but we dealt with that well, and that was important."