Manchester United player Greenwood, 18, and Manchester City player Foden, 20, are reported to have been in a room with two girls in Iceland at the weekend, following England’s victory in Reykjavik, and as a result will not join the rest of the squad for Tuesday’s game against Denmark.
Good Morning Britain presenter Morgan, 55, ranted: "They're young men who knew the rules... why was there not enough security to protect them for themselves?
"They're living the dream for teenagers and young people. And now they're going to miss their first game because they have to be shamed. They're covidiots."
Greenwood and Foden’s breach of the England team’s bubble, put in place to protect the players from contracting COVID-19, was confirmed by England manager Gareth Southgate.
Morgan had earlier tweeted: “Their selfish reckless stupidity is bad, obviously. But how were they able to do this? Footballers need babysitting - by security guards - to protect them from themselves.”
And the TV presenter also clashed with his own son on social media over the incident.
Spencer Morgan tweeted in response to the news of the footballer’s actions: “Literally who cares...”
To which his father replied: “I’d imagine all the people they have now massively inconvenienced with their selfless, reckless behaviour including their England & club colleagues who have abided by the rules to ensure football matches can be played.”
England manager Southgate said in a statement: "Unfortunately this morning it was brought to my attention that two boys have broken the COVID guidelines in terms of our secure bubble and we had to decide very quickly that they couldn't have any interaction with the team or travel to training.
"Nothing has happened in the areas we occupy in the hotel. We are still getting to the depths of all the information because this was only brought to my attention a couple of hours before training, so I'm still getting to grips with the detail.
"What is clear is there is a breach of the COVID-19 guidelines. The whole squad have really followed that to the letter. I'm not going into any more details until I'm aware of everything."
Foden has released a lengthy apology on Twitter, saying: “I am a young player with a lot to learn...
“On this occasion I made a poor decision and my behaviour didn’t meet the standards expected of me...
“I will learn a valuable lesson from this error in judgment and I wish Gareth and the team good luck this week.”