Yes, you can fix it.
Carbon Fibre is no different to working with fibre glass. All you need is the right resin and some carbon fibre matting.
Clean around the area as best you can using sandpaper. Mix the resin and apply around the hole on both side. Put some thin polythene sheeting on the outside (viewed) surface and tape it down tight - this gives you a nice flat finish to the resin you've just applied.
Now on the reverse side, place you shaped piece of carbon fibre mat to close over the hold and work more resin into the matting and around the surrounding area.
Leave to set overnight.
Sorted!
I buy my stuff from
http://www.cfsnet.co.uk/ buying "West Systems" resin (the Junior pack will be plenty at 10 quid) and carbon fibre matting at 15 quid per square metre.
Depending on the size of the hole, you can buy cheaper carbon-fibre tape, which is the same as the matting but in thinner strips at 2.50 per metre.
Hope this helps!