Games not to resign!

So, I'm a very low-level player, but this was a fun one. In this game I was playing (very badly, even by my generous standards of "badly") white, and blundered my way into a situation where my king was vulnerable, my opponent had two rooks to my one, most of my minor pieces were tied up defending one another, and both my one remaining rook, and one of my bishops were simultaneously attacked, so there was no way to avoid losing a piece. Faced with this disaster, I resigned.

But the evaluator reckoned I had a substantial advantage. Investigating, I find that if I'd saved the bishop, and left the rook hanging, there was a most delightful mate just waiting. Maybe good players would spot the mate easily, but I didn't see it.