Ozil saw a weak spot-kick saved by Manuel Neuer in the early stages of the first leg of his side's last 16 tie against the UEFA Champions League holders.
Things soon went from bad to worse for the hosts, who saw goalkeeper Wojciech Szczesny dismissed for a foul on Arjen Robben, with David Alaba missing the resulting spot-kick, before goals from Toni Kroos and Thomas Muller left Arsene Wenger's side with a mountain to climb in the second leg in Munich in three weeks time.
On Thursday, Podolski took to his official Facebook account to give public backing to compatriot Ozil, who bore the brunt of criticism following the game.
"Everybody is disappointed because of yesterday's result," said Podolski.
"However, that's football. It's not fair to diss (disrespect) Mesut. Criticism is part of sports and this is good, but picking one player out doesn't help the collective and the whole club neither!
"He's an outstanding player who will make all of us happy in the future.
"A missed penalty won't change that. This happens to me and to every footballer. Friends stand together. So let's go!"
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