I am in a situation where the hiring manager of a position I interviewed for knows my current manager. This connection made my manager aware that I had applied for a role.
Unfortunately I did not get the role. This is making my situation with my manager awkward. How do I deal with this?
Is this for an internal transfer? This is unfortunately the risk you run into when you pursue a transfer without alerting your manager. That's why I recommend talking to your manager when thinking about a team switch (assuming you have a decent or better relationship).
Things will be awkward from now on. Personally, I wouldn't bring it up and just do as good work as possible. If your manager does ask you about it, I would go for a "It's not you, it's me" strategy. Give your manager credit for what they've done and spin the move as you looking for a new opportunity to explore, learn, and grow (instead of leaving a team which you don't like).
Here's another good thread about this general topic: "How can I gracefully leave my job?"
I think what I am worried about more is that my manager knows I got rejected and so the feeling of “not good enough” is kicking in. I have this fear that my manager may hold this rejection of me against me for future promotions/ raises etc justifying the fact that I was not good enough for another position I interviewed for. The position interviewed for was roughly similar to what I am currently in but my contract with this position is coming to an end soon.
Interesting, I was more thinking along the angle that your manager now knows you want to leave their team.
Interviews are tough and random. Hopefully your manager knows this and doesn't count this rejection against your personal character, but if they do, there's not much you can do.
The best route forward as with many cases is to continue doing great work and building up trust + relationships (particularly with your manager). Hopefully that's enough to get your contract renewed.
Best of luck!