A brace from alvaro Morata and a goal from Pedro propelled the hosts to victory, but Hodgson insisted he was pleased with his side's display regardless of the scoreline.
"I don't think we were in any way battered by Chelsea today. We gave it our best shot," he told 'Sky Sports' after the game.
"I don't think, quite honestly, we were under the cosh by any stretch of the imagination.
"The two strikes of Morata's were very clinical. They took their goals well.
"We played well enough to get back into the game and scored an equalising goal.
"They got the free-kick for the second goal and that puts you on the back foot. They were all well-taken goals."
The defeat leaves Palace sitting just three points above the relegation zone, with games against Tottenham and Manchester United up next.