The Norwegian defender will miss three matches after his dismissal for a two-footed challenge on Lee Cattermole in the first half at Craven Cottage last Sunday.
But while the Cottagers felt the tackle didn't deserve to see Hangeland sent off, they would have risked extending his ban by a further match if they had tried and failed to get it overturned.
"We have not appealed the decision," Jol said. "I felt it was very harsh, but there is always a risk and I didn't want to take that risk.
"If you appeal, they can make it four games instead of three but I still think it was harsh.
"If you saw the Emmanuel Adebayor's challenge (against Arsenal), it was different and you can't compare the two challenges so I think three games is too much.
"We have to cope with it. We have to come up with different solutions.
"We don't have another Hangeland. We have Philippe Senderos and hopefully, if he is still fit, he will come in and replace him.
"Hopefully Aaron Hughes and the players we have got are strong enough because I saw them against West Ham. It is quite a challenge."
Hangeland won't be the only absentee for Fulham when they travel to Stoke on Saturday - Alex Kacaniklic, Bryan Ruiz, Kieran Richardson and Mickael Tavares are also ruled out.
Simon Davies is still not yet able to return to training, though Jol is able to call upon the services of Mahamadou Diarra and Chris Baird again.
Meanwhile, the Premier League club have allowed goalkeeper David Stockdale and striker Marcello Trotta to go out on loan to Hull and Brentford respectively.
"We've got a good connection with Hull," Jol said of the Stockdale deal.
"I know Steve Bruce and if something happens to Mark Schwarze I can always call him back.
"That is the agreement so there is no problem. He was desperate for games and I think he needs to play and keep his rhythm.
"Trotta had different plans. He didn't want to go to the lower leagues before so we talked to him and I think understands that it is a nice opportunity for him to get games and to play because he is a very young player."