The Palace defender left the field in the 43rd minute to be replaced by Martin Kelly.
Speaking with Palace TV, Hodgson said: "He's injured his groin. He felt a pain in his groin so it's obviously some sort of strain in the groin.
"I expect we'll have to wait until [...] they do the scans to find out how serious that is. But it's obviously a massive blow because we don't have other full-backs at the club other than Joel and Patrick and we can ill-afford to lose them."