The Chelsea full-back, who made 107 appearances for his country, decided to retire from international duty after being left out by Hodgson.
Hodgson will reveal his 23-man squad on Monday, but Cole has lost his place, likely to Everton defender Leighton Baines and Southampton left-back Luke Shaw.
The experienced Hodgson said leaving Cole out was a difficult decision but he wanted to be as respectful as possible by letting the 33-year-old know before the announcement.
"Among many difficult decisions I've had to make for my squad, not selecting Ashley was one of the hardest," Hodgson told the Football Association's website.
"He's been an incredible competitor for England, to amass over a century of caps is a truly staggering achievement and he deserves enormous credit for the desire and brilliance which has shone through over the years he has represented his country.
"There are few players who can be considered among the very best in the world but Ashley in his prime was the best left back without question."
Hodgson praised Cole for the way he handled the news and said he was keen to look to the future.
"The most important factor was speaking to Ashley prior to the announcement on Monday, he deserved to hear it directly from me and he took the news with huge grace," he said.
"In two years working with him he has shown nothing but relentless professionalism, and a great hunger to play for England. He is someone I have the utmost respect for and I wished him all the best, he in turn wished the team well this summer.
"Of course I must respect his decision to retire, he has been one of England's finest players, but I want to look to the future.
"It has been one of the hardest decisions of my career."
