I totally caved

Let me start by saying that Emma is an awesome kid. I couldn't have been blessed with a happier kid, who most of the time minds and gets along great with everyone. Well.....here lately she HAS had some listening issues. When she told me recently that she took a hearing test, and passed, I knew hearing wasn't her problem. She knows the rules. Knows how many times she should have to be asked to do something, but she's been "testing" the waters a bit lately. I know this is completely normal, but I know it's up to me to make sure it doesn't get out of hand. I've been telling her that I'm going to have to start taking things away from her when she doesn't listen. So, night before last we were cleaning her room and she kept doing something over and over that I had asked her not to do. I told her that was it, and she would not get to watch a movie at bed time. Now, Emma is just like me, and I know it's a bad habit, but I have to fall asleep with the TV on. Turn it on, I'm out in 5 minutes, turn it off, and my mind starts racing. At first she was ok with the idea, but it was hours till bed time. Bed time rolls around and she's pretty good, at first. I read her a book, I laid with her a little while, and finally I left her room. A long while later, she hollered for me. Of course she was still awake. She's just like me. I laid down with her and she started crying "I just want my DVD player"...this went on and on....I tried everything. I scratched her back, I spoke calmly to her and told her I understood that she wanted it, but she has to learn to listen, I sang to her...I tried it all. Finally, James came in the room and we both wondered if it was worth pursuing it at that point. She had already felt the pain of having something taken away from her. We talked to her and she knew why I didn't want her to have it, she understood everything, but I totally caved in. I gave in. This is exactly what I didn't want to do. I felt bad for her being so upset, but I felt bad about giving in too. Did she already learn the lesson ? or did she learn some tears would get her what she wanted ? I really don't know.....for me, this is the part of parenting that's the hardest. I feel like I failed a little....