It's not making a mistake that matters, it's what you do after you make a mistake.
On a coworker's last day with the company, I asked him to share some advice our team of developers. This was one of his three points:
You will make mistakes... sometimes huge ones... sometimes you will delete a month of work with the only option being to start again (true story). It's OK, part of the process, how you learn and often a large reminder to slow down.
I absolutely love this, but want to elaborate on it.
The main point is the important part. We're all going to make mistakes. They will come in various shapes and sizes, and will have varying degrees of consequence. But one thing is constant — they will happen. Everyone makes mistakes.
Your boss, partners, clients, and stakeholders have all made a lot of mistakes throughout their career. Like quote from above says, it's all part of the process. But what makes a difference is how you react and act following a mistake.
How you react immediately should be as calmly as possible, while also taking responsibility for your actions, subsequently dealing with any consequences that come from it.
That's the being a good person part of making a mistake. But then it's time to move on. It's time to roll over the mistake and do something about it. To learn from it such that you not only don't make the mistake again, but you also get better at your job as a result of making the mistake.
For example, this is the story of deleting a month's worth of work mentioned in the quote. In it, our quote author owned up to it, but learned something new as a result. And he never made that mistake a second time.
So, don't put too much pressure on yourself. Slow down. Pay attention to the details. And when you (inevitably) make a mistake, own up to it, roll over it, then learn from it, and get better.
The three most important lessons learned over a few decades as a developer.