Was the patch used or a new one?
If used how long had it been used for?
Fentanyl is a potent opiod and the patch formulation makes it easy to absorb the drug across mucous membranes (gums & tongue).
It can be fatal if absorbed in high quantities.
The usual recommendation if the pup ate the patch isn't showing symptoms yet is to induce vomiting. BUT ONLY INDUCE VOMITING IF SHE IS BEHAVING NORMALLY. Dogs that are symptomatic have already absorbed too much and could aspirate their vomit and die.
Give 1 tablespoon of peroxide per 10 pounds of body weight. Then take her out and run her around to get the peroxide bubbling. She needs to get rid of the poison. If no vomiting in 10 to 15 minutes repeat the dose. You can give the peroxide directly or with a little canned food or bread chunks.
If she vomits the patch then follow up with 1GRAM (not milligram) of activated charcoal per pound of body weight every 6 hours for 2 doses to bind the drug & block absorption.
If she doesn't vomit the patch or is showing symptoms (lethargy/sedation, pinpoint pupils, incoordination, slow respiratory rate) an emergency clinic visit is best to monitor and maintain blood pressure, for heart monitoring, and to give the reversal agent, naloxone.
With prompt appropriate treatment they usually are fine, but untreated they can die secondary to a low heart and respiratory rate and low blood pressure.
Please let me know if you have any further questions.