A game where both sides have a king and knight is a draw game. There is no way for either side to get a checkmate (you can try playing it out yourself, but trust me, there is no checkmate with a single knight; there isn't even one for a king and two knights). So this game should have been a draw already, but because there was a time factor, someone had to lose. I'm sure the reason your opponent didn't accept that draw was probably because you were low on time.
In a non-timed game, this would automatically be considered a draw, but because there was a time factor involved, someone had to lose. Hope this helped.
http://www.chess.com/livechess/game.html?id=12628165
Obviously, this is a blitz game with many errors. My opponent won on time... when I got down to a knight each, I figured I was safe, but the clock kept running! Is it because, say, I had my king on a1 and my knight on b1 and his king was on b3, if he moved his knight to c2 I'd be mated? I tried offering draws but he wouldn't take them, even though this was our second blitz and we had friendly conversation between games :/
To be honest, if I was on the other side, I might have let the other guy lose to gain a few rating points, but I have decided I'll try not to be like that from now on.