That Nasus didn't know what he was doing if he lost that badly to you. I main Nasus so I may be slightly biased but Jax is an easy farm lane. All he had to do was stay behind his minions and take farm while you pushed him under turret.
Typically Jax will run out of mana much faster than me and I can free farm while he backs. If you harass me I will back up letting you take minion damage whilst the wave pushes in my favor. I will then freeze under turret and stack happily until my jungler shows up. At this point I will wither you and throw spirit fire ahead of you guaranteeing you lose armor and the trade. If we don't kill you, you will at least have burned flash and be low enough to have to recall again.
A few problematic champs that are AA bases are Riven (if she is really good) or Fiora (again if really good) B/c if they time their mobility right they can harass and make it back in the bushes while taking little to no minion harass.
Also did you look at his build in your match history? He had all AP runes... It's no wonder you stomped the hell out of him...