Hodgson's contract was due to expire at the conclusion of the finals, and the shock 2-1 defeat in the second round in Nice prompted the manager to announce his departure.
"I'm going to read a statement, so I will not be misquoted," he said.
"I am extremely disappointed about the result and our exit. We haven't progressed as far as we were capable of and that's unacaceptable.
"We were the youngest team, which is both exciting and remarkable. I am pragmatic. My contract was up after the Euros and that is it. I will not continue.
"My staff joined with me and they will leave with me. I would like to thank all the support staff, the fans, the players. It has been a fantastic journey and I look back at it with pride.
"I am sorry to exit in this way, but that is the way things happen. I still hope we will see an England team in the final of a major tournament in the near future."
After reading the statement, Hodgson immediately left the news conference and there were no further questions.