The current crop of Under-21s this month became the latest in a long line of teams to fall short of the nation's expectations.
The Young Lions headed into the European Championship among the favourites but became the first team to exit the competition, leaving Israel without a point.
"We haven't performed as well as we could have done, certainly not as good as we played in the group stages," Under-21 left-back Rose said.
"I know the players have been getting a bit of stick but I'd like to think we are all in it together.
"We were when we were winning, so we all should be when we are losing. It's very disappointing and very embarrassing.
"I don't know why people automatically expect England to be contending for these competitions and winning them.
"We last won the World Cup in 1966 so I don't know why people put this expectation on England at all. But there is no excuse for not winning a game.
"I think the expectation should drop a little bit, definitely."
The inquest into England's failure in Israel is well under way and could see Stuart Pearce replaced as Under-21s boss.
The former international left-back's contract expires at the end of the month and is odds on with the bookmakers to be replaced.
Asked if the players had let him down, Rose said: "Definitely. He has put his trust in a lot of players, especially me.
"We don't know if this is going to be his last game, so to not win and not get a point is a real let down for him. That's what we have done."
Jordan Henderson, Jack Butland and Andre Wisdom have all expressed their desire for Pearce to stay on, with Connor Wickham another to back him.
"Of course [I want him to stay]," the striker said. "He gave me my debut at Under-21 level a few years ago.
"Every trip I have come on he has treated me with respect and has encouraged me.
"He has kicked me up the backside a few times when I have needed it - that is what you expect from a good manager - that is what he is. I have the utmost respect for him."