The faucet adapter included with my new portable dishwasher won't hook onto my faucet?

I just got a new Danby portable dishwasher, but the faucet adapter included to hook the hose onto the faucet won't attach. It's designed for threaded faucets, and mine isn't threaded. I think it's an older faucet. I rent, so unless its absolutely necessary, I don't really think I can/want to replace the faucet. Could I find another adapter that would work with my sink? How do I know it will fit? I can't exactly bring my faucet to the hardware store. I let all my dishes pile up in anticipation of the new dishwasher, so I'm stressing out a bit about the mess. I really need to fix this SOON!