Walcott went to hospital for scans after the incident, and Hodgson said that Simoncini should have been punished.
"In normal circumstances he would have been sent off and we would have gone 1-0 up from a penalty earlier on," Hodgson told BBC Sport.
"We have had a bad injury which I'm very disappointed about. Had the referee given the penalty and sent the keeper off, which he should have done, we would have scored more goals."
England have seven points from their opening three Group H fixtures.