Omniserv, the firm employed by Edinburgh Airport to give special assistance to reduced mobility passengers, launched an investigation into the incident along with the airline Easyjet.
At the time, Edinburgh Airport said it was "unacceptable".
The CAA said Edinburgh's rating was principally down to the poor performance of the previous assistance provider, Amey, and a lack of proper oversight by the airport.
A spokesman for the airport said: "Since the findings of this report were collected six months ago we have - as noted in the report - taken great steps to improve in this area including bringing in OmniServ who won a three-year contract to undertake the provision of services for persons with reduced mobility at Edinburgh Airport.
"Edinburgh Airport is absolutely committed to continuing to improve the passenger experience of everyone who uses the airport, including those with a disability and those with reduced mobility."
Amey said it decided not to bid for the new contract to operate services at the airport.
A spokesman for the company said: "We are proud to have provided assistance to over a hundred thousand passengers with reduced mobility over the life of our agreement with Edinburgh Airport.
"We welcome the news that subsequent investment has been made with regard to equipment and staffing levels to address the issues raised in the report."
Glasgow, the highest-ranked Scottish airport, was rated "good", while Aberdeen, Glasgow Prestwick, Inverness and Sumburgh were described as "taking steps".
Matthew Buffey, the CAA's head of consumer enforcement, said most disabled passengers were happy with their experience.
"Our research shows passenger satisfaction with special assistance at UK airports is high with 85% satisfied or very satisfied," he said.
"However, high standards are not always universal, and occasionally things go wrong for disabled people and those with reduced mobility."
He added: "These passengers are very much dependent on airport staff providing the appropriate assistance so it's a really important task for airports to get right."
The CAA said it had introduced a new framework for measuring how well airports help those who need extra assistance.
The tests include how happy passengers are with the assistance provided and how long they have to wait.
They also look at how well airports consult with disability organisations.