Arsene Wenger's team were embarrassed at Allianz Arena on Wednesday, leaving them on the verge of yet another last-16 exit.
But Koscielny wants Arsenal to believe heading into the return leg at the Emirates Stadium on March 7.
"In football, you never know," the French centre-back said, via the club's website.
"We are professional, we have a second leg and we will try to win. But after a game like this it's very difficult.
"But we'll fight because we are professional and we play for Arsenal."
Arsenal were level at the break in Munich, only to concede four goals after Koscielny came off injured.
But, like Wenger, Koscielny struggled to explain just what went wrong for the Premier League club after the break.
"I don't know either," he said.
"I think the first half was good - we were deep, like you need to be, and tried not to give them space or opportunities to score.
"It being 1-1 at half-time was good for us but after we conceded the second goal, I think we needed to stay more compact because we had a second leg at home.
"When you can win [there], you need to stay together, defend together with all 11 players and keep this.
"We didn't. Bayern played very well - they have some top-class players who can make the difference in front."