Rooney, 26, agrees that lessons now have to be learned - although he believes Hodgson does have the tools to succeed with England.
He said: "We have got to learn to keep possession better because although the game was quite even, in terms of chances that's where Italy dominated.
"When you see teams like Italy, Spain and Germany, they win games by dominating possession.
"That is something we have got to bring into our own game.
"The manager worked a lot on getting us organised and on team shape. I think we are already a better team than when he first took over.
"But he's only been in the job a short time and I am sure we are not yet playing the way he wants us to."