Their achievement on Sunday did come with consequences, however, as both Scott Dann and Jason Puncheon went off injured, compounding the squad's fitness woes, with the likes of Joel Ward and Mamadou Sakho already out.
Palace are due to play Southampton on at St Mary's on Tuesday, and the match will be their third in six days.
Hodgson is hoping to have Ruben Loftus-Cheek and
"Sakho's likely to be out for a few weeks to come with a quite serious injury, Joel Ward is still recovering, and there's no sign of him recovering in the next few days, and then we've lost Scott Dann, we've lost Jason Puncheon.
"I'm afraid we've stretched our resources to the absolute limit. That's why it was very nice to see three players who've not had many chances, Jaido Riedewald, Tim Fosu-Mensah and Patrick van Aanholt come in and do as well as they did [against City].
"We will recover one or two players who were unable to play, before the Southampton game.
"Scott Dann's injury doesn't look good, that's for sure. It's a serious knee injury. How serious it'll turn out to be we'll have to wait and see."