Norway international Hangeland was dismissed after 31 minutes for a two-footed challenge on Lee Cattermole with the game still goalless.
Jol felt his captain had not gone in maliciously on Cattermole and said he would like to see referees use more common sense when making such decisions, saying: "I think he was probably the only one in the stadium who really thought it was a red card."
"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, he (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."
Sunderland boss Martin O'Neill's opinion on the sending off was the polar opposite of Jol's and he admitted he was surprised at the number of dismissals still resulting from two-footed challenges.
He said: "It is amazing when we have been given the directives. I don't know how many times we have been told about it, we have been guilty ourselves with Lee Cattermole being sent off, sometimes I don't understand players' minds. I don't think if you don't go in two-footed that anybody is going to consider you a coward, in fact quite the opposite."
O'Neill saw his side win for the first time in seven league games and was pleased with the way his players used their one-man advantage.
"I'm delighted to win the game, sendings off change the dynamic of matches, we saw it yesterday in the Tottenham v Arsenal game," he said. "You have to try and take advantage of that and we did that in the second half.
"They were never out of the match but I was pleased for us to score some goals and win away from home, our goalkeeper has made two fantastic saves and he is having a fantastic season, and I thought Fletcher was fantastic too."