Thanks to everyone first of all for your replies, they are appreciated. I've gotten to thinking more about exactly what happened and more specifically what my question really is, so allow me to clarify:
I believe what happened is that I didn't kick out the crab fully from a slight crosswind. The ball was centered (something I'm always aware of), and what happened was that I landed not pointing directly down the runway. Then what happened was, when I went to straighten myself out by using the rudder, the plane started dancing a bit and my instructor was quick to tell me to knock it off with the rudder pedals.
So while I understand what happened, it got me to thinking (and this is what I originally was wondering): if I do land going with the airplane oriented perfectly straight down the runway, will it continue to go perfectly straight after touchdown, or should I expect to have to use some rudder input to keep going straight down the runway?
The reason why they started putting nosewheels on airplanes was so that they would tend to straighten themselves out after touchdown- that is, begin rolling in the direction they were moving when they touched down, even if the nose was pointed slightly askew. There's more mass in front of the mains than behind, so if the plane touches down crooked, that greater mass will come towards the center as it pivots on the first wheel to touch down (which, we hope, is the upwind wheel).
But it's important that the direction mentioned above be on the runway centerline, or at least parallel to it, so some interplay of aileron (for drift left or right of center) and rudder (to keep the airplane's centerline aligned with the runway centerline as much as possible) is needed most of the time, when there's a crosswind.
Ideally, when there's a crosswind,you want to touch down in a perfect sideslip, totally negating the effect of the wind, so that the trike gear doesn't have to help you. But nobody's perfect, and in fact, sometimes you can only sideslip so much in certain conditions, and you will end up "crabbed" a little as the mains touch down.
This is why most taildraggers have a lower demonstrated crosswind component than nosewheel planes of the same weight, etc.