The Norway international was dismissed after 31 minutes for a two-footed challenge on Lee Cattermole with the game still scoreless.
Second-half goals from Steven Fletcher, Carlos Cuellar and Stephane Sessegnon secured Sunderland's first league win in seven attempts, although the substitute Mladen Petric had levelled for 10-man Fulham.
Martin 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.
"I think he was probably the only one in the stadium who really thought it was a red card," the Fulham manager 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, 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."
The Sunderland manager Martin O'Neill's opinion on the sending off was the polar opposite of Jol's and he said 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."
O'Neill said he 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."
Adam Johnson also put in his best performance since moving from Manchester City and O'Neill reckons he is starting to adjust to life at Sunderland.
"He was playing in a team at Manchester City where he is getting 20-25 minutes in matches to try and do something or coming on when they are in front, they are a terrific side," he said.
"Here he is having to start the matches, with respect to us we are not remotely as good as Manchester City, so he is having to strive, he is having to do more for us and he is getting there."
Jol, who will now be without Hangeland for three matches, also lost Alex Kacaniklic and Bryan Ruiz to hamstring injuries during the match and confirmed both are likely to be out for at least three weeks.
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