"I can fully understand the reactions from many of you and I myself am absolutely gutted," Kiessling said on his Facebook page after his so-called phantom goal helped his team to get a 2-1 win.
"After seeing the replays on television, I can clearly see that it was not a legitimate goal.
"During the game, after heading the ball and turning my head, I did not exactly see whether the ball had gone into the goal or not. Somehow, the ball was lying in the goal and I said exactly that to the referee.
"I'm sorry for all sports fans... Naturally, it's not nice to win like that. Fairness is important in sport, for us in the club and for me personally."
The confusion arose when Kiessling's 70th-minute header flew just wide of the post, hit the side-netting and ended up in the back of the net to put Leverkusen 2-0 ahead.
He initially put his hands on his head when the ball went wide and looked confused when the referee awarded the goal and his team mates ran to him to celebrate.
The Bundesliga does not use goal-line technology, which a FIFA source said would have spotted the mistake, or the additional goal-line assistants who are used in European club competitions.
A replay was ordered after Bayern Munich were awarded a goal against Nuremberg in similar circumstances in 1994.