Hart is England's most capped goalkeeper and the only man with previous tournament experience, but Southgate has elected to go with Jordan Pickford, Jack Butland and Nick Pope.
"Joe played in most of our qualifying matches, he's been a big part of the England team the last few years, and he's a valued member of the squad," Southgate said.
"But in the end, I've got to look at performances over the last 18 months with their clubs, and the three lads we picked were the three best goalkeepers in the league this year.
"I pick players on form and, if he's playing well for his club, why wouldn't we select him?", Southgate continued when asked if there was a way back for Hart.
"There's no reason for this to be the end. He has an important career decision this summer and I hope he can be back at his very best."