You can get the entire kit at Walmart which includes jag, bullet puller, patch worm, brass brush and mop for about $8. First off, Cayugad is correct. Second, if you have a patch down in the breech your rifle will likely not fire. But I don't think you did any harm to your rifle. What you are seeing is probably just flash rust and should wipe right out of your bore.
Here is what I suggest if you don't have a patch worm right now. Take the largest diameter rifle brush you have (or even better a .410 brush) and put it on the end of your rifle cleaning rod as the thread is prob different than your ML rod. Twist it clockwise so as not to unscrew it and see if it will catch the patch and pull it out. Then swab your bore with hot soapy water then rinse with hot clear water. Dry the bore with dry patches (you will likely see the first patch or two come out looking rusty but this is just more flash rust and is only on the surface and wipes right off) followed by an alcohol patch then dry patch. The a light coating of a quality gun oil and you should be good.
I use this process and never had any problems. For a gun oil, after the alcohol patch I like to use Montana Xtreme Cowboy Blend which always seems to remove just a bit more residue in the bore and then coat the bore with Montana Xtreme Bore Conditioner.