You can stuff some batting in it then use an iron on patch, or sew soem material on with a hook needle, I would clip the burnt areas off though, so it doesn't smell. I'd also put a mattress pad over it.
Dont' forget to turn the iron off after you're done.
Seriously I'm really glad nothing more was burnt! My house burned down a few years ago and it's an awful thing to go through. Take care!