The fullbacks were useless because of us being unable to bring them into play - as a result of how weak we were in keeping possession further up the pitch. That last-minute chance, the Rooney overhead kick, was the result of us keeping possession in advanced positions for long enough to work the fullbacks into the game. I'm not saying we played particularly well, because our offensive players should have done more to relieve the pressure, but we very obviously played - and this is true of the tournament as a whole and our warm-up games - with a defensive strategy, based around absorption of pressure and maximizing our few chances (we had the highest chance conversion rate in the tournament) after the group stages.
You're right about Rooney, though. He did a decent job on Pirlo early on, but started to drift. It was dumb.
"two balls hit the woodwork" - iirc both were chanced, long-range shots. Certainly the first one was. Had Marchisio scored the goal of his life in the first couple of minutes, well, it's not like any team can legislate for that.
"another goal was called offside" - because we played an effective offside trap. That is nothing but our defence doing their job. The fact that the goal was ruled out is irrelevant; he scored it illegally because we made him score it illegally.
tl;dr: Our tactics allowed Italy to have the most possession and chances, which seems to be the criteria you/others are using for "domination". That said, we could and should have done more to relieve some of the pressure - our offensive players just spectacularly failed to perform.
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