The Three Lions failed to win a game in Group D as they recorded their worst showing at the tournament since 1958, with Costa Rica and Uruguay progressing to the last-16 stage.
|12/1||England are 12/1 with William Hill to win Euro 2016|
"I said England would struggle but that's not football knowledge, that's just common sense," Keane, who is assistant coach at both Aston Villa and Republic of Ireland, told reporters.
"If you look at the squad, they should have done enough to get out of the group. The players didn't perform.
"[Republic of Ireland] played Costa Rica last month and if you had told me then they would top the group I'd have said you were mad.
"But if I look at the England squad and the players then a lot of them still lack vital experience. Whether it's Champions League experience or big-game experience.
"A lot of those players are yet to win a trophy and yet people still expect them to go to the World Cup and reach the quarters or semi-finals.
"People are ranting and raving about the younger players – they still have a lot to do. We can argue all day about winter breaks and all the rest of it, but the fact is they should have done better."
The former Irish international went on to defend ex-club team-mate Wayne Rooney, claiming the England striker would continue his international career despite criticism of his performances in Brazil.
"If you think Wayne Rooney's gone, then you are sadly mistaken," he said. "I thought he did OK. I'm sure he will feel that he should have done better. Top players are quick to look at themselves."