It was a tale of two halves. I wasn't paying close attention in the first half, but England tried to sit on the lead after halftime. Italy was dominating them as you stated. Sometimes it requires a little luck to score, as they did on the equalizer. They played well enough that they could have easily won it in regular time as England rarely was on offense.
OP's summary is revisionist propaganda.
I have no horse in this race, was mildly rooting for England since they never win anything.
Even the British commentator said England was shell-shocked (IIRC), and stated that Kane and Sterling were barely touching the ball for the bulk of the second half.