Your opponent was out played by you. I play the Ruy Lopez often. You didn't cheat. I think you went easy on him truthfully. I think you could have been much harder on him in the earlier parts of the game. He made a few mistakes at the end and it gave you tactics that were the difference.
If you have chess.com analyze it, it will show your mistakes, blunders, etc...it is one of the fastest ways to prove you were a human playing and didn't play above the GM level or any where close to a titled players level. It can be the fastest way to not only shut him up, but to exonerate yourself, now that you've meantioned it.
In an otherwise unremarkable game the opponent suddenly called me a "computer user" before resigning. What could lead him to this conclusion, except for bitterness?