Despite reservations from United manager Louis van Gaal, it was widely expected Shaw would be named in Gareth Southgate’s side for the tournament.
But Southgate said the full-back “medically was not fit” to play next month, adding some clubs objected to fitness or injury issues being released publicly.
Shaw missed Manchester United’s draw against Arsenal last Sunday because of fears he suffered a concussion from James McArthur’s flying arm in the previous weekend’s game at Crystal Palace.
And Hodgson insisted there was no rift between the Football Association and Old Trafford staff.
He said: “Gareth Southgate has had lengthy discussions with the club and they have made it clear to him that, at this moment in time, Luke is not in a medical or physical state to play, so he has been left out.
“I am not happy because I love Luke Shaw and think he is a very fine player, as do Manchester United, so we were hoping he would be fit and raring to go.
“I would have been disappointed if he was not in my squad, but if he was in Gareth’s squad I would have wished him all the best.
“I am very disappointed he can’t make it but hopefully he will come back stronger for the new season and we will get the benefit from him from August.”
He added: “I am very confident about that (no club versus country battle).”
Another United player who will not feature this summer for The Three Lions will be Ashley Young despite an impressive end to the season.
Hodgson said the winger was not picked in the squad for the friendly with the Republic of Ireland on June 7th and the Euro 2016 qualifier in Slovenia due to an injury concern.
He said: “We made soundings with the United medical department with regards to Ashley and they led us to believe there was a slight issue with him which does need to get cleared up over the summer, so on this occasion we decided it was probably not the right moment to ask him to come back.
“I certainly have not called time on his (England) career as far as I know, so we will see how it goes in the future, and I congratulate him on the latter part of the season with Manchester United, where he has played very well.
“We are not blind to the fact he has played well but on this occasion we have preferred to stick with the ones who have been with us since Ashley last played, and also the medical department at United have informed us it might be better for him to use the summer to get over the minor problem he has had.
“If you want to know more about that you will have to speak to Manchester United.”