Well let's start with this:
Who do you commonly pick? Some champions don't have a snowballs chance in hell at slowing Nasus down. Irelia, Malphite, Shen, Cho'Gath etc aren't really going to slow him down. They can be annoying, they can brawl a lot but they won't flat out deny him.
In fact, I think the idea of "denying" Nasus is a bad idea in the first place. It's 2015 in league of legends, unless you're playong extremely snowbally champions who kill the enemy every time they see them once they get ahead and thus, deny them by the virtue of killing them over and over, nobody really gets denied. Global gold, objective gold so on make it too hard to do this. Your goal isn't to deny, it's to slow him down. An average Nasus in a good lane will get 300 bonus damage on his Q by 20 minutes, you want to crank that down by about 100-150. Even 250 isn't that bad.
You need to also realize that Nasus is actually at his best mid game, not late game. Mid game, if he's able to get some farm, he's most effective in teamfights. He will usuaiy have 1-2 tank items, enemies will have no armor or magic pen (unless grossly fed), enemies will be under leveled since he's a solo laner and as a result their will be much longer, so he's harder to kite and kill. Flat armor pen is probably at its best at this stage too, and the base magic damage from his E and Ult can be pretty big mid game too. This is what you want to deny, and you CAN deny this from happening.
Nasus' spells aren't spammable at all early either and aside from his q, his mana costs are high. His q is 20 at all levels but wither is 80 at all levels and spirit Fire is 75 at level 1, increasing by 15 each level. And his E and W cooldowns are both 15 seconds a piece at level 1, spirit fires base CD never changes and withers CD drops a second for each point. He also has the worst base mana pool of any champion in the game and his base mana regen isn't great either. Point is, he can't trade much so he has to play from a position of defense early (don't mistake this for he can't trade because he can, you just can't force the issue every time).
There are chamoions who beat him in lane and champions who just outscale him in teamfights. Champions who easily handle him in lane are champions like Gnar, Olaf and Darius. Champs like Rumble, Swain, Lissandra, Azir, etc can easily slow him down. Champions like ChoGath, Singed and Trundle can't really stop his farming, but they can legit shit on his teamfight and hold his split push forever because of their wave clear and absurd late game tankyness making them practically impossible to die.
Without knowing who you're playing, I can't rightfully say what you should/shouldn't do. But I can say rushing a last whisper is terrible, you should never do this under any circumstances. I don't know who you played so that's as far as I can comment on that. And really, I don't have much else to say.