MacBook Air 13" Mid 2012 Battery
Chris, I just did the same thing to mine and had the same result. I wish I'd read your warning first! Perhaps some heat at the center of the plastic backing would have helped release the adhesive from the chip/backing.
To anyone attempting this fix, if you feel anything in the center of the plastic back cover sticking, do not force it off. It might be possible to get a blade in there to slice through the adhesive, but it really didn't take much force at all for the chip to break free of the circuit board.