Caveat: This post is about punishment for poor behavior or rule violations. Not all D/s relationships have a discipline aspect to them, however, those that do have their own set of unique situations - like how to accept punishment. This is just my experience.
KnyghtMare and I have a discipline dynamic. While I avoid punishment like the plague (and I think you should too) there are times when I've violated a rule or behaved badly and he needs to teach me a lesson to bring myself back to where I should be. As a submissive, when a punishment is looming, I spend a lot of time stressed and riddled with anxiety and guilt. It took years to learn that when the punishment was over, I was to be purged of all of it. Hopefully, what took me so long to learn will give you some bits of wisdom for your own journey.
First, let's review punishment. If you have a dynamic that includes punishment for misbehavior then you'll have to face correction. Punishment in this situation is not fun. It's not meant to be for play and it shouldn't be enjoyable for either party. Punishment often fits the crime, so to speak, but in some dynamics, there is a set punishment for behavior correction. KnyghtMare prefers to avoid corporal punishment because we both enjoy that for play, so my punishment is often the removal of privileges like TV time, computer use, and furniture use. All of which really stink, but serve their purpose.
If you do use corporal punishment, then it's often the case that the tool used will be different than one used during play. There may be a ritual to punishment such as having to count, a formulaic apology (I have one of those), or the requirement to be stoic and silent during punishment. Whatever the case may be, how you accept punishment is what this discussion is about.
What do I mean by accepting punishment?
Trusting your partner to make judgment calls as far as your punishment. You've submitted to this person so you must have some level of trust with them. You've negotiated a punishment dynamic so that includes trusting them to make the punishment fit the crime and to decide if and when punishment should happen.
Receiving your punishment without pouting, tempers or complaints.
Remind yourself that you consented to this and that you did something to warrant this punishment. Throwing a fit about how unfair or inconvenient it is isn't going to help your case any.
Acknowledging that once the punishment is over, the slate is wiped clean.
I'm guilty of this one, we walk around feeling full of guilt and remorse long after the punishment is over and it drags down any ability to move on. Learning to embrace forgiveness is hard, especially for yourself.
Not reverting to guilt over your infraction or anger over the punishment.
You are the one to blame for your infraction and outwardly displaying anger on someone else for what you did is wrong and childish.
It took me about five years to really begin to accept punishment as gracefully as I suggest above. It's not as easy as reading this post and nodding along. But the beauty of learning to accept punishment is that the discipline and punishment dynamic works when you both take your own roles seriously.