As well as exiting at the quarter final stage, England endured a disappointing tournament off the field as several players encountered disciplinary problems.
Since then Martin Johnson has been removed as head coach as part of a number of changes to the RFU at boardroom level.
"It is important for any team to show humility, especially when you are winning. I thought a number of England players undermined this in the arrogance they showed," Robinson told the Mail on Sunday.
"They know who they are and it was not across the board, but unfortunately the whole squad got tarnished.
"You need self-belief in players, of course, but you also need to possess some humility, and a number of players overstepped the mark."
Robinson, who is now head coach of Scotland, faces England in the Six Nations opener on February 4.