An important aspect of mindfulness is acceptance, or of avoiding harsh judgments. Acceptance means being able to be aware of our experience without either clinging to it or pushing it away. Instead we accept our experience with equanimity.
All too often we find it difficult to accept what we're feeling. A common pattern is to experience some initial unpleasant experience, and then to feel bad because of feeling bad, and then to feel bad about feeling bad about feeling bad, and so on. It's a vicious cycle of feeling bad about feeling bad. The feelings are generated by thinking in unhelpful ways, so this means there are several approaches to breaking the vicious cycle.
Acceptance of what you're feeling is one tool, although it's not so much a tool as a way of being. Acceptance means acknowledging what you're feeling, and standing back from it so that although you experience the unpleasant emotion you don't entirely define yourself by it.
Then there's the whole area of the thoughts. When you feel bad, your mind generates thoughts that are conditioned by the unpleasant feeling. These thoughts ("Here we go again. I don't want to feel like this. I can't stand it. If I feel like this no one will like me. I don't think anyone likes me anyway") are what make us feel bad about feeling bad. We take a molehill (or at least a hill) and make it into a mountain.
It's very useful indeed to learn to stand back from our thoughts as well as our emotions. We can recognize that our thoughts are just thoughts, and not reality. When you notice thoughts arising, you can let go of the stream of thought. Thoughts only keep going as long as we put energy into this, so by letting go of the thought we're actually withdrawing energy from it and stopping it from being perpetuated.
Labeling thoughts as thoughts can be useful. When we notice ourselves thinking we can just say the word "thinking" quietly to ourselves. When we name our experience we again create a small gap that gives us a sense of freedom.
You can adopt a skeptical attitude about your thoughts. Our thoughts often lie to us, and we can feel empowered by choosing not to automatically believe them. Instead of believing thoughts like "No one will want to be with me if I feel as bad as this" we can simply be aware of this as a thought.
I love the bumper sticker on the bulletin board in Cynthia's office that says, "Don't believe everything you think." It's really worth it to put in the effort to learn to accept without judgment. Don't expect this acceptance to happen automatically. A deep willingness to let go of judgment is the first step. Then we practice - slowly, consistently. And be sure to affirm yourself everytime you do let go. That positive reinforcement will be supportive of subsequent attempts to accept without judgment.