I've admitted defeat, even to myself.

Literal

Self [even-でも] lost.

Very terse introspective statement. 自分でも means 'even to/by myself' — the particle でも combining で (by/with/to) and も (even). This makes the sentence about conceding to oneself — an internal acknowledgment of defeat. The verb 負けた is past plain form. Subject omitted as usual.