You didn't tell us what OS X you are using and your profile doesn't tell us.
You didn't tell us what version of Java you installed, but it sounds like perhaps it was Java 7 from Oracle which would mean you are running 10.7.3 or above.
If you didn't previously install Java 6 or migrate from a previous system that had it, you many be out of luck. Some have suggested installing Java for Mac OS X 10.7 Update 1, but I have not seen confirmation that it works. Java 6 is no longer publically supported by Oracle and I doubt that Apple will continue much longer.
Keep an eye on this site to see when the next Zero-Day exploitation of Java shows up http://java-0day.com.