Last weekend the Eagles became the first side in English top-flight history to lose their first five league games without scoring a single goal, an unwelcome record that was extended to six games today at the Etihad.
Hodgson's side did well to keep out the free-scoring hosts for much of the first half, conceding their first of the afternoon just before the whistle when Leroy Sane fired home.
The result was made comprehensive in the second period, however, as Raheem Sterling with a brace, Sergio Aguero and Fabian Delph all added to a goal tally that has now seen City score 16 times in their last three league games.
"I thought at half time to come at 1-0 down is a bit unfortunate. I thought we'd played some good football," Hodgson told reporters afterwards. "Two quick goals then and when they get a few up, with their quality, passing and movement it becomes very difficult.
"The goal before half time was very damaging. We didn't defend anywhere near as well as we should have done for that goal. We looked reasonably dangerous on the counter-attack but when they go 1-0 up we have to score. In the end we have been heavily beaten.
"We know there is a lot of work to do with this group and they know that too. I am learning about the team all the time and they are learning. There were elements missing from our game today that we have to instil. Today was a harsh lesson.
"Our focus has to be in May. By the latter part of the season the players must know what we are looking for. They should themselves feel stronger by then. In the short-term these kind of defeats are staring us in the face as we are playing quality teams."
Palace's hopes of an upturn in fortunes in the near future look bleak as they must now face Manchester United and Chelsea in their next two league games.