We started to lose the ball and couldn't get forward.
England, meanwhile, finished fourth at the tournament, their best finish since.
Italy were awarded a penalty.
It took an Italian set piece to create the first big chance but Giorgio Chiellini's expert header was brilliantly tipped over the crossbar by Ugurcan Cakir.
The match broadcast by drew an average of 2.
In doing so, England became the first team in European Championship history to win their group after scoring only two goals.