First things first. Regardless of who made the error, it's your return and you signed it, so you're going to have to make it right with the IRS no matter what other course of action you pursue.
Now onto getting some relief on your end...
With respect to whether your CPA should pay, that really depends on the circumstances. Give your CPA a call and see whether he/she is amenable to working out some kind of solution - some tax pros offer a limited guarantee.
If your CPA refuses to cooperate, you can consider consulting with a litigation attorney or go to small claims court. That said, unless it's a serious error where the CPA is clearly at fault (this may be difficult to prove), litigation to recover fines and penalties may cost you more than it's worth. And I feel pretty confident saying that you won't recover any unpaid taxes - you would have been responsible for those even if the error hadn't been made (the penalties and interest are another story).
All of that said, I'm not sure how sizable the error is, but generally the most cost effective solution is to request an abatement of the penalties directly from IRS. The most common way to do this is to fill out an IRS Form 843 - you can also make the request in person.
Good luck.