Hodgson was forced to apologise for using the saying, made famous by space agency NASA, to urge his team to pass to Andros Townsend during the Three Lions' 2-0 win against Poland on Tuesday.
The Society of Black Lawyers have since demanded race appreciation courses for Premier League managers, and Allardyce has offered sympathy to the England coach.
"I do feel sorry for Roy, as it was a slip of the tongue, it happens," Allardyce told the Daily Mail.
"It wasn't mean to be offensive, but the world is unforgiving these days. And it's a shame this week because they were two great results (against Poland and Montenegro) and it's forgotten because of this."
Tuesday night's victory secured qualification to the World Cup for Hodgson's side.