I have never come across an airline website which did not have flaws which might lead directly to an incorrect booking. And one of the most dangerous things you can do is to go back and try to check that you have input the correct information.
As I remember it, even the best airline website is capable of changing your airport of origin if you choose the most unfortunate sequence of events.
If it happened to me I would try to work out why the booking was wrong by trying to repeat the sequence of events and then write to the airline explaining why I felt entitled to a refund.
If the letter looked reasonable I would post it. And if the response was not satisfactory the Small Claims Court (in England, not Scotland ) has always worked well for me.
And if you have any doubt about a booking, start all over again.