The 23-year-old was pictured inhaling the substance, popularly known as laughing gas, from a balloon during a night out with friends.
While not illegal, usage of nitrous oxide can prove fatal, and Walker issued an apology for his behaviour on Twitter on Monday.
"Now I know the health risks, it was poor judgement on my part," he said.
"I won't be doing this again and hope that no-one else is influenced into putting their health at risk by my actions."
The Football Association said it would not be taking action against the player and Hodgson said he was prepared to draw a line beneath the affair.
"I am happy, he has made his apologies and admitted a mistake," Hodgson said, during a press conference prior to England's World Cup qualifier against Ukraine in Kiev on Tuesday.
"It was a long time ago, he'd forgotten it. It would have been much worse had it happened this weekend."