Wolfgang Stark has apologised to Borussia Dortmund following their 3-2 defeat on Saturday.
The Bundesliga champions were winning 1-0 and dominating the game when the referee opted to award a penalty to Wolfsburg and send off Marcel Schmelzer for handball - a decision that ultimately turned the match in the visitors' favour.
“I've looked at it again later and unfortunately it was an error of perception on my part," he told reporters outside his dressing room.
"I'm sorry, that should not happen. The penalty and the red card were a mistake on my part. That's annoying."
Midfielder Diego converted the penalty and, with the home side down to 10 men, Wolfsburg went on to win the game 3-2, much to the annoyance of Dortmund coach Jurgen Klopp.
"The consequences were bizarre," he said after the game.
"We were 1-0 ahead and Wolfsburg had no chance and then comes the game-winning move. It was a brutal decision. The boys have to chop their hands off to avoid risking a handball.
"I had everything taken into account, including the penalty. But the red card decided the game today. Until then we were vastly superior."
The defeat means BVB now trail league leaders Bayern Munich by 14 points.