The former Fulham and Liverpool manager admitted he was not impressed by the atmosphere at Villa Park when Manchester City and Chelsea met in the Community Shield on Sunday, in comparison to what occurred in stadiums at London 2012.
Hodgson said: "I wouldn't mind a spotlight also focused on the crowd because I think one of the things that made the Olympic Games for Great Britain was the incredible support within the stadia where the events took place.
"Maybe we need to start looking not only on the field and off the field after the match, but maybe in the stadia itself.
"To be frank you can't compare the atmosphere and the way people behaved in the Olympic Stadium with the game I watched the day after, the Community Shield.
"It was a very different public at that game to the public our athletes performed in front of."