The Gunners' club-record signing apologised via Facebook for what proved to be a costly error when his chipped spot-kick was saved by German goalkeeper Manuel Neuer after eight minutes in the Champions League last 16 first leg clash at the Emirates Stadium on Wednesday night.
The Bundesliga side went on to win 2-0 after goalkeeper Wojciech Szczesny was sent off for clattering Arjen Robben in the box. Although their resultant penalty was also missed, second-half goals from Toni Kroos and Thomas Muller all but ended Arsenal's European ambitions for another season.
Ozil made a promising start following his £42.5million signing from Real Madrid at the end of the summer transfer window, but has struggled to make an impact in the last few months.
Wenger says the latest setback must not be allowed to play on the Germany international's mind.
"Is he over it now? Certainly not, because 48 hours is a short time to get over that, but it is part of the job as well to deal with disappointment and to show that you can respond to it," the Arsenal manager said ahead of Saturday's Barclays Premier League clash against Sunderland.
"He apologised after the game, but I don't think people are shocked by the fact that he missed a penalty because Bayern missed a penalty as well.
"He takes his penalties in an unusual way so people are maybe a little bit less understanding, but everybody can miss penalties.
"It is his way, you accept it or not. It's his way of taking penalties like that."
Ozil is not Arsenal's designated penalty taker, sitting behind Mikel Arteta and Olivier Giroud, who were both not playing on Wednesday night.
Asked whether he would let Ozil take a penalty again, Wenger said: "I believe that at the moment you have to let him recover from that.
"I had examples before, with people like Dennis Bergkamp who missed an important penalty in 1999 and refused after to take any penalty (for a while).
"Incidentally he (Bergkamp) gets a statue (at the Emirates Stadium) on Saturday, so that doesn't take a statue away from you and some other people don't mind and (take penalties) again.
"It depends on how you feel and how much you want it."
Arsenal will be without full-back Kieran Gibbs because of a hamstring injury, and Wenger is likely to rotate his squad.
Giroud had been left on the bench against Bayern Munich in favour of rookie forward Yaya Sanogo.
The France international was in the headlines for some personal issues in the past couple of weeks, but Wenger insists the 27-year-old is in the right frame of mind.
"We all have our weaknesses and strengths, some of us when we have problems outside the field, use the pitch or the work, to forget about our problems. Some of us are different, but he is one of them who will focus completely on the pitch," Wenger said.