"I am shocked," Kompany, who missed the tournament with a thigh injury, wrote in his column in The Times. "Looking from the outside, I honestly can't work out how it happened."
England crashed out of the tournament at the round-of-16 stage in humiliating fashion on Monday, losing 2-1 to the smallest country ever to compete at the Euros.
The 30-year-old Kompany, who has played either with or against every member of former England manager Roy Hodgson's squad during his eight-year stint in the Premier League, was at pains to explain why the talent in England's ranks had performed so badly.
"What I do know is that when people respond by saying the players "aren't good enough", they are wrong," he said.
"You cannot tell me that the Harry Kane you see in the Premier League isn't good enough or that Raheem Sterling, Wayne Rooney, Joe Hart, Daniel Sturridge, Jack Wilshere, Chris Smalling and others "aren't good enough".
"England had one of the strongest squads at Euro 2016 and yet something happened on Monday, a psychological "event", to cause them to perform like that. It looked like something got to them."
The defender said the team's lack of a clear playing style had contributed to their downfall.
"That was an England who I didn't recognise," he said. "This England team are capable of playing a different, more possession-based style... but there always needs to be a balance and, to me, it wasn't there against Iceland."
Hodgson quit as coach after the result and Kompany said his replacement should have the experience, hunger and ambition to re-establish the team's identity.
"I want to see an England team playing like an England team... they need to get back to doing some of the things they do best," he added.
The defender signed off by asking for protection for England's players, who have been fiercely criticised in the British media.
"People need to get away from the blame culture. Don't blame the players.
"You can't tell me that players like Hart and Rooney don't care. They care as deeply as the players for Belgium, Wales, Italy, Iceland or anyone else.
"Technically they are good enough. The commitment is there. What I still cannot explain is the psychological event that happened."
