In Sonic Adventure 2, when you rank poorly in a stage as Shadow the Hedgehog, he says "I guess I'm not at full power here" and there is no further elaboration. Maybe try something like that?

When you design your characters, try to consider how they'd respond to failure. Everyone makes mistakes, even experts. If you can't imagine them failing, maybe you need to rework something.

If your character starts at level 1, be extra mindful of this. A level 1 adventurer is not an accomplished expert, but they might try to pass themselves off as such.

I understand. I like playing characters that take themselves seriously, but you still have to RP a failed roll. In any case, I think the one embracing the goof should be the player, not the character.

For example, if I fumble while trying to stealth, I could say that my character is impatiently shushing the group or that an alarm on his phone goes off or something like that. Not absolute incompetence, but something that could have been avoided.

If your character thinks it's could not be their fault, you could have him point fingers at someone else or some other thing. Needless to say, don't actually blame other players and know your table.