Frankly, it doesn't make any sense to me that Booster let Batman in the door. Booster tried to *zap* Batman when he revealed Ted's shattered goggles, and rather justifiably blamed Batman for Ted's death.
Diana was one of the few people who listened to Ted and tried to help, so it's odd that she's acting like she didn't try. If she just admitted she fails sometimes, and this time it was disastrous for one of her friends, it would be a more believable moment for me.