So, when you do break a promise, you have a tough road ahead of you if you want to rebuild trust. Most of us perform poorly in this situation and make matters worse. We become defensive, justifying our actions by explaining how we were "forced" to do something, or by claiming your team members misunderstood your promise. Don't do this. It erodes trust even more.
Instead, start with a simple question: What are the consequences of what you have done? Ask your team how your actions impact them, and really seek to understand the problems you have caused. Then, apologize. Let them express anger about it, and don't try to defend yourself. It's not such a bad thing to admit you have made a mistake. It is much more humanizing to be fallible than it is to pretend to be perfect.
Once you understand the problem you've caused, ask what you can do to make it better. If you have embarrassed the team to others, go and speak to them and set the record straight. If you did what you felt was right, even though it broke a previous commitment, talk about it openly. Breaking a commitment is a problem, but so is honoring an unreasonable one. Try to reset expectations based on what you've learned since you made the original commitment, then be more careful of making "never" and "always" commitments.
Don't be uptight about admitting you screwed up. Most people expect professionals to defend everything they do to the death. Be the one person who isn't that way, and others will respect you and enjoy working with you.