The Hoops have loaned the Sierra Leone forward to the Swedish club for 12 months but don't want him to play in when the two sides meet in the third round of Champions League qualifying.
Nilsson feels the Scottish champions are at fault for not inserting a clause into Bangura's contract to disallow him taking on his parent club.
"It is a Celtic error. They should have put it in the contract when he came on loan," he told SunSport.
"I don't know if they didn't do their research but it is their mistake, they have to live with it.
"I have been on loan to three clubs and in those loan agreements it is standard to have a clause saying you won't play against your club.
"I would be extremely surprised if he did not play against Celtic.
"If Celtic had demanded that clause in the contract then Elfsborg would not have had a problem with it. Now they have this situation and have to live with it.
"As a footballer you want to do well for the club you are at. You have to think about where you are playing at that moment."