The Manchester United striker, along with Manchester City youngster Phil Foden, was sent home from international duty after they invited Icelandic girls into their hotel room, bursting the coronavirus bubble the squad were in.
Both players missed the subsequent Nations League match against Denmark as a result and Hodgson feels that there should be further punishment for the error of judgement.
‘I’m afraid that when you make a mistake as big as he made, you should be expecting to pay a price for that,’ the former England manager told talkSPORT.
‘The fact is that if you’re old enough to come in and hold down a regular spot at United and called up for England,
‘I’m afraid you have to produce the level of behaviour that is required at that level.’
Greenwood issued an apology for his behaviour while away with England, and is yet to suffer any further punishment other than being sent home from duty and miss the Denmark match, which ended goalless.
‘Having now had the chance to reflect on what’s happened, I can only apologise to everyone for the embarrassment I have caused,’ read a statement from Greenwood.
‘It was irresponsible of me to break the COVID-19 protocols which are in place to protect players, staff and the public.
‘Playing for England was one of the proudest moments in my life and I only have myself to blame for this huge mistake.
‘I promise my family, the fans, Manchester United and England that this is a lesson I will learn from.’
The 18-year-old has issued his second apology this month after a video emerged of him inhaling laughing gas from a balloon.
Manchester United take on Crystal Palace in the Red Devils’ opening Premier League contest of the season this Saturday and the young striker will be desperate to prove himself on the pitch again.