Pearce is expected to pay with his job after England left the tournament without a point.
"Have we let him down? Definitely," said Rose, who played for Pearce at three Under-21 tournaments. "He has put his trust in a lot of players, especially me. We don’t know if (Tuesday) was his last game, so to not win or get a point is a real let down for him.
"That’s what we have done (let him down). We haven’t performed as well as we could have done and certainly never played as we did in qualifying. I know the players have been getting stick but I would like to think that we are all in it together.
"We were when we were winning, so we should all be together when we are losing. It is very disappointing and embarrassing, really. It is hard to put a finger on what has happened. The preparation was second to none.
"The manager makes sure that is always the way, whether it is a qualifier or a friendly. I can’t fault the preparation and I can’t fault the manager. It is just hard to put a finger on but there is no excuse for not winning a game."