Palace striker Odsonne Édouard canceled out Mohammed Kudus' opener for the Hammers on the day.
Hodgson said: “I thought that for a large period of the game, I was quite pleased with the way we were playing, both defending and attacking. It was certainly an even game in that period of time, especially right at the very beginning – we started extremely well.
“Then, we had to go through the anxious moments of the final five minutes of normal and additional time. That's understandable, because we've just lost two games with late goals, games where we felt we gave away the point we'd earned.
“We were playing against a crossing team, so I could have done without that ten minutes which I thought was when West Ham were at their most dangerous, but I also think the team showed a lot of resilience. I could understand the anxiety.
“It was more important we come away with a point today, because had we lost this game with another late goal, it would have had massive consequences for the team's confidence and feeling about themselves. But if we think back to the way we played for the whole of the 90 minutes, I think we could be pretty satisfied with the point we've taken here today.
“I thought our first-half performance was quite good. I thought we were organised, I thought the players were in their right positions, I thought that we moved the ball around quite well.
“Maybe in the second-half we went a little bit too direct at times, trying to make things happen that bit too quickly in terms of our attacking play, but putting the two bits together…
“In the second-half, there was the resilience, a fighting spirit, a passion. In the first-half I thought there was a little bit more composure in our game, but put the two together, it's got us a point here today - a point which is never easy to get."