After a positive first-half display, Arsenal were hit by a double setback early in the second half last night.
Gunners captain Laurent Koscielny was sent off for a foul on Robert Lewandowski and the Bayern hitman scored the resulting penalty.
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It was to be the first of five Bayern goals in a 30-minute second-half capitulation as they eventually won 5-1 and 10-2 on aggregate.
And Hummels feels Arsenal could have defended more rather than continuing to attack.
Mats Hummels defends against Theo Walcott
He said: "That's an opportunity.
"You just say: 'Ok, we take this 1-1 or we take maybe a 1-2.'"
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Hummels also felt the controversial decision to award Bayern a penalty changed the match.
The Arsenal players were dejected
"Of course the red card and the penalty was the decision today," he added.
"It changed the whole game. I think Arsenal did a good job in the first 45 minutes – even up to the chance from Giroud in the second-half.
"They had opportunities to make it very close tonight but with the red card, the game was over. Everybody knew it."