"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."
Schmelzer was judged to have handled the ball to stop Bas Dost's goal-bound shot going into the net but replays showed that ball hit Schmelzer's knee and, although it also brushed his fist, the contact was insignificant and clearly unintentional.
A penalty was awarded, Schmelzer sent off and Diego converted the penalty.
As so often happens, the decision completely changed the course of the game as Wolfsburg, losing 1-0 and completely outplayed before the incident, went on to win 3-2.
Dortmund became the latest victim of soccer's so-called triple punishment - when a player who denies the opposition a clear scoring opportunity concedes a penalty, is shown the red card and then has to serve an automatic suspension.
Widespread criticism of the measure turns to outright indignity when the decision which leads to the threefold sanction is shown to be wrong.
Saturday's incident was also notable for the unsporting behaviour of the Wolfsburg players who protested en masse when the ball hit Schmelzer's knee, provoking bad feeling between the two team benches.
"The consequences were bizarre," said Dortmund coach Juergen Klopp, who refused a handshake from opposite number Lorenz-Guenther Koestner at the end.
"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," he said
A FIFA working group led by former Germany captain and coach Franz Beckenbauer, which has now been wound up, suggested replacing the red with a yellow card except in the case of dangerous tackles.
The proposal was studied by soccer's rule-making body, the International Football Association Board (IFAB) in March, and was put on hold.
Klopp said he could have put up with the penalty but the red card unsettled his team.
"I had everything taken into account, including the penalty. But the red card decided the game today," he said. "Until then, we were vastly superior." (Writing by Brian Homewood in Berne; Editing by Ken Ferris)
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