On the back of the guitar, remove the plastic cover over the trem claw springs and tighten the two trem claw screws to lower the bridge back to where it was, and/or add more springs. A little trial and error, re-tune, and tighten or loosen the screws as necessary. You won't mess anything up by adjusting the truss rod as long as you use the correct Allen wrench and take it easy, it is for setting the amount of bow in the neck, affecting string height above the fret board. If you adjust and the setup is wrong, you can adjust it back to where it was. Check the setup guide for a good starting point to understanding the adjustments. These aren't hard-and-fast rules, you can adjust for your individual tastes. Experiment and learn and have fun.

http://www.fender.com/support/articles/stratocaster-setup-guide

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---> "The amp should be SWITCHED OFF AND UNPLUGGED before you do this!" <---

Por favor, disculpe mi español, no se llega a la práctica con mucha frecuencia.

If it's just the springs as mentioned, you can tighten the claw and/or add springs and/or change the angle of the springs. I did exactly the same thing last night after buying a used strat. I took the bass side spring and middle and ran them from the 2 bass most side holes on the block and the 2nd and 3rd claw points. Then ran the treble side spring and went from the farthest most treble side on the block and one in on the claw. Worked great and the trem stayed down.

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2002 mim Telecaster
Jimmie Vaughan Stratocaster
Mexican HSS Stratocaster
6 non-fender guitars
2 kids (not for sale)
1 wife (uh....no comment)