Norway international Hangeland was dismissed after 31 minutes for a two footed challenge on Lee Cattermole with the game still goalless.
It proved the turning point after a bright start by the hosts with second-half goals by Steven Fletcher, Carlos Cuellar and Stephane Sessegnon securing a 3-1 victory and Sunderland's first league win in seven attempts.
"I think he was probably the only one in the stadium who really thought it was a red card," Jol said.
"It would have been nice if most of the referees had played football themselves, it would be nice if sometimes they could make decisions in the spirit of the game.
"I can't remember having a red card at this club. Hangeland is a nice boy and told me it was not intentional, he slipped. I won't say that it is a common thing for him because I haven't seen him do this tackle."