Natasha thinks that normally, she'd be embarrassed to fight in public, but she doesn't notice anyone but Daniel. He puts his head in his hands and Natasha wishes she could keep pretending. She thinks she should've told him from the beginning, but she didn't know that she'd feel this much.
It's noteworthy that Natasha identifies truth as being a major help to intimacy, given how secretive she's been all day. This shows again that her attempt to keep her issue private was a way for her to protect herself from heartache.