The Premier League outfit impressed in the opening 15 minutes of the game and should have opened the scoring when Ozil was awarded a spot kick after being felled by Jerome Boateng.
However, Manuel Neuer - who had earlier thwarted Yaya Sanogo - saved his compatriot's penalty before Bayern seized the initiative, and Kroos was relieved to see the Germany No.1 keep the scores level early on.
"We rode our luck in the first 15 minutes, especially with the penalty. Obviously, it would have been a great deal harder if it had gone in," Kroos told reporters. "I think that after the first five minutes, when we weren't quite in the game, we got the upper hand even when Arsenal still had 11 men. But then, of course, you're going to dominate a bit more when you're a player up.
"We're well aware it's not over by a long shot, as we saw last year. It was a step in the right direction but we're by no means through yet. We won 3-1 here last year and then it was much closer in the return leg, so we have been warned. That's why there are two matches, nothing is decided after the first one."
The return takes place at the Allianz Arena on March 12.