Kiessling's 70th-minute header flew wide of Koen Casteels' right-hand post during the Bundesliga fixture at the Rhein Neckar Arena, but the ball ended up in the back of the net after going through a hole in the side-netting.
Hoffenehim coach Markus Gisdol was left furious after the match and called for the game to be replayed, and Kiessling has now apologised to fans on his official Facebook page, admitting the goal should not have stood.
"Dear fans, friends and all those who just write to me," he wrote. "I can understand the reactions of many of you one hundred per cent and am myself quite upset.
"According to the reps (repeats) on TV I see it so clearly: it was not a regular goal. In the game I have not exactly seen in my header and the turning of the head, whether the ball went into the goal correctly or not.
"Somehow the ball was in the goal. Exactly what I told the referee.
"I'm sorry for all sports fans and the course of the game. To win so of course is not good. Fairness is important for the sport in our club and for me personally."
Leverkusen boss Sami Hyypia admitted after the match that he was "uncomfortable" to have seen the replays of the header.
"I celebrated during the game because it looked like it was in, but of course now it's a bit uncomfortable," he said. "But I can't do anything about it - it's the referee who makes the decisions."
Former Germany international Rudi Voller, meanwhile, was less than sympathetic towards Friday's hosts, stating: "Hoffenheim have spent such a lot of money on a nice stadium. Maybe next time they should buy some proper nets."
The win moved Leverkusen to the top of the Bundesliga table, two points clear of Bayern Munich, having played a game more.