I'm not saying she wasn't a compelling character, but her physical weakness and moments of vulnerability in comparison to the big guys highlighted how much of a boys club it is. It isn't that there isn't a role for her, it just seems that there should be a woman on the team who doesn't need protecting when the real shit hits the fan.
She was trapped in a confined space with the freaking HULK! Anyone in their right mind would be shitting themselves. The fact that she managed an escape, with an injured leg no less, and managed to stay relatively calm is a testament to her character. The manipulating with tears thing was just that: manipulation. She was playing at weak in order to trick Loki into revealing his play, and it worked.
Also, big freaking explosion and Cap has a shield that will completely deflect it. Had he been right next to Hawkeye, he would have been protecting him.
Honestly though, every single one of the Avengers had to be rescued by another at some point. But because Black Widow has some actual character, has vulnerabilities and isn't just an ice queen, that somehow makes her weak and unfit to be there?