Couple of things, was the fuel petcock set to "Pri", "On" or "Res"? There is no Off. Should be set to "On" [lever down IIRC, I'm running a Pingle]. this will allow the vacuum diaphragm in the petcock to shut off the gas supply when the engine stops. "Pri" is for "Prime", if the bike has been sitting a long time and the fuel has evaporated from the carb bowls, then "Prime" bypasses the vacuum control and pours gas into the bowls [no vacuum from engine needed]. Should only use this to get bike started, then switch to "On". "Res" is "Reserve", when running in the "On" position and the gas gets too low, the bike will start to stutter like its out of gas [which it effectively is at that point. "Reserve" lets you tap into the last gallon in the tank so you can get to a gas station.
All that being said, if you were running in prime, it would be fairly easy to blow past the float needle valves. Theoretically they should be able to handle the pressure, but as they get older they don't seat as well. Couple of suggestions:
1) DON'T TRY TO START THE BIKE!! Okay, that's a little stronger than a suggestion. What can happen in your situation is that liquid fuel will build up in the #1 cylinder [it's the lowest when the bike is on the stand] and when you try to start the bike the liquid won't compress, leading to a bent rod. Many examples of that on the site, search the threads.
2) Make sure gas isn't continuing to flow, and then pull the plugs and crank the bike over to expel any liquid gas that's in the cylinders. Make sure you unhook the plugs from the wires and keep the wires as far back on the bike and away from metal, you don't want a spark to ignite any gas coming out of the cylinders.
3) After your sure the cylinders are clear, change the oil. If your petcock is working correctly, you should be able to set it to the "On" position and ride the bike. If gas continues to drip or accumulate in the airbox, you'll probably need to rebuild the petcock and/or carbs. Luckily for you, there are members on the site that do both; contact Markus56 about rebuilding the petcock, and WickedZL900 about rebuilding the carbs. Both do excellent work.