I am currently extraordinarily lucky to be in my second season of a recurring guest star role on a show run by one of the best show runners in the business and some of the most crazy-professional and skilled cast and crew members I've ever worked with. I'm learning a LOT.
Recently, we were in the middle of a take, and I screwed up a line. I pushed through and we finished, but as soon as the AD yelled, "CUT," I said "ACK! I screwed up, sorry!"
Immediately, the show's lead leaned over to me and said, "I didn't notice anything. Never admit you screwed up unless you have to." A minute later, the director came over to me, took me by the shoulders, looked me square in the eye, and said, "No apologizing. We're all in this together."
They were absolutely right. I let my gratitude for the job turn into fear about doing well, and saw myself as a less-than-equal member of the team. It's an easy trap to fall into, especially when you care about what you're doing and have worked long and hard to get there. But because it's the kind of project where everyone cares about what they're doing and worked hard to get there, they wouldn't let me get away with it. They reminded me that I'm there because I deserve to be, we're all working toward the same goal, and as long as I'm giving my best, I have nothing to apologize for.
You don't have to have a role on a fancy project to put that advice to good use. Whenever you're doing something you care about, it's tricky to strike a balance between being grateful for every opportunity and humble enough to recognize that you have something to learn, and remembering that you're there because you have something unique and valuable to offer, and part of your job is to own it.
(Of course it's also possible to focus too much on your own value, and forget to be grateful and humble. At some point, you'll work with someone who does things they should apologize for, but doesn't. Instead of getting helpful advice from their peers, those people tend to just stop getting hired.)
Think about where this balancing act applies in your own life. Do you have a tendency to err too far on one side or the other? Is there someone in your life who does a good job of striking that balance whom you can model yourself after? And where can you practice shifting that balance now, so you're prepared when it's time to do it under pressure?
Spend some time sloshing around in this potentially uncomfortable question. Think of it as an investment in your future, so when you do get the chance to work on a great project, you'll be grateful, humble, and every bit as proud and confident as you deserve to be.