Hitzfeld angry with Lichtsteiner dismissal
Hitzfeld berated Lichtsteiner after he was given a first yellow card for dissent but said the second booking was a mistake by the referee.
"The second offence was not a yellow card, the replay showed that Lichtsteiner played the ball," said the German after his defender appeared to trip James Milner.
"I'm angry at the first as we know that Italian referees don't like players making disapproving gestures and Lichtsteiner plays in Italy, so he should know what to expect."
Hitzfeld, who won seven Bundesliga and two Champions League titles in an outstanding career at club career, has found the going tougher since moving on to the international stage two years ago.
Although he qualified Switzerland for the World Cup, they managed only one goal in their three games and were knocked out in the first round, despite beating eventual winners Spain in their opening game.
Lichtsteiner's dismissal in the 65th minute came as the Swiss, trailing 1-0, were producing their best spell of the game. England increased their lead four minutes later.
"The sending-off came as we were attacking," said Hitzfeld. "Xherdan Shaqiri scored a dream goal to give us hope but England waited and played on the counter and they did it very well."