But Hodgson has dismissed suggestions that Eze should be dropped and the midfielder is in the Palace squad to face Arsenal on Thursday.
Eze was caught attending his former club’s third-round defeat to Fulham on Saturday when he failed to wear a mask at all times and was not socially distanced the in the directors' box.
Hodgson has said the 22-year-old showed “naivety” and made an “error of judgement”.
Last week Hodgson promised “very strong consequences” for further breaches of Covid rules after Luka Milivojevic after Palace captain attended a New Year’s Eve party, but the Eagles boss has said Eze is available to face Arsenal.
"It was very disappointing,” Hodgson said. “It was a lot of naivety on his part to think he was OK to do those things. It obviously isn't.
"He has apologised and will learn a harsh lesson from it and we will have to act internally to make sure it is a lesson well and truly learned.
"Does what Eze did deserve leaving him out? I don't think so. But it does merit a fine. We take this very seriously. We don't want our players breaching coronavirus regulations.
"I think he did it naively and foolishly, not a determined gesture to break a rule but he did. We're not happy at all and we show that by fining him.
"I'm not a big fan of that over the years, but on this occasion, I think this error of judgement deserves it and he has to be cautious not to make them again."