Palace missed a stoppage-time penalty as Manchester City extended their unbeaten run with a goalless draw at Selhurst Park.
Hodgson was delighted despite his side's late penalty miss.
"I'm very proud of the team's performance," he said.
"I know how difficult it is to play a team of Manchester City's quality... it was a very pleasing performance and an excellent point.
"Before the game we would have been jumping through hoops at having claimed a point, then you get a penalty late in the game, so there is an element of sadness at a chance missed.
"But I've said to the players: 'continue that level of performance week after week and we've got a good chance of staying in the league'."