Spider mites, ouch.
If those were the only problem, and they've already sucked the seedling leaves brown and dry, it might be too late.
Until someone more experienced comes by, consider some of these remedies:
Spray with a hard, stinging mist of water, like you would get from an irrigation mini-jet sprayer running at 40+ PSI. Knock off as many as possible! Be sure to spray up form underneath, down from above, and in-and-around everywhere those mites laid eggs. repeat often!
Also swab with soapy water, trying to wash them off AND kill them with normal soap.
Repeat fairly often. Can you dunk the leaves completely under soapy water?
Spray heavily with insecticidal soap. Probably more than once, every ... ummm ... weekly? You have to kill them as they hatch from eggs.
Potent chemical insecticides. I guess malathion is now available only as a war gas, so that's out.
Pyrethrins? They are thought to be more "green" since they were originally derived from Chrysanthemums (now produced industrially.) And they are biodegradable and less toxic to humans than many insecticides.
Start new seeds and think about what environmental conditions might discourage them next time. I THINK they like dry leaves, and frequent hard-mist-sprayings knock them down (or maybe just discourage them with humidity - I don;t know.)