Paul and Samantha Jackson and their two children briefly stopped in a private car park at Exeter Airport before catching a flight.
The family said they drove away as soon as they were told it was the wrong car park but were later charged.
Premier Park of Exeter which operates the "Park 2 Fly" car park said it has to deter people abusing the site.
Mr Jackson said he pulled into the car park at 05:51 BST because he "did not want to stop the car on the main road" with two children in the back to get his car park paperwork from the boot.
He said: "I went to see the security guard in the car park to inquire if we were in the correct car park, and he told me I was in the wrong place and gave me directions to the correct car park."
The family, from St Austell, pulled out of the car park six minutes after arriving.
Mr Jackson said: "The parking charges for Park 2 Fly is £15 per day, this works out 0.0625 for the 6 minutes we were in the car park."
The Jacksons have written to the company to explain why they stopped and have the option of making an appeal.
A spokesperson for Premier Park said: "The car park does not have a security guard as it is an unmanned site, so we are unsure who Mr Jackson spoke to on arrival.
"There is a massive sign at the entrance and other signs around the car park stating what the charges are.
"We allow time for people to quickly read these signs and leave. We have so far not received an appeal from the family, but any appeal will be looked at if it is submitted."
A family has been charged £100 for pulling into the wrong airport car park for six minutes.