Friend in Bronze thinks he won against me in a 1v1.

Ok, so, I 1v1'd my friend the other day, and usually when 1v1ing, its either first blood or first tower. In this case, I got first blood against him, and then I asked if he wanted to still play because I had to go soon and if I wanted to still player before I had to go sleep, and he said sure about still playing. He eventually kills my nexus, because I was vsing a Darius as Riven. After the game ends, he thinks he won when clearly when you get first blood or first tower in a 1v1, you usually win but no, he thinks he won because he thought I said first to tower wins. Who do you think is right? Me or him?

EDIT: We just talked it over on skype, saying how we have our own opinions, so if he think he won, he won, but I think i won so I won, and I told him, lets just move on, and we're going to