I have published all my PhD papers independently, how get a postdoc position?
I would recommend considering these options:


Try to write or formulate your own project. Some funding agencies, e.g. ERC Starting Grant requires you to have at least one important 
publication as main author or without the participation of your PhD supervisor. You already achieved it, so it might be benefited.
Don't take it personally. They may have better applicant (=somebody matching their needs better) and they tried to find some reason to reject you. Very probably all other points were excelent and the authorship was only one suspicious think. If they didn't read recommendation of your supervisor then they didn't made their homework; not you.
Endure this period between PhD and postdoc and continue to apply for other opportunities and improve in soft skills too. Positions for highly qualified people are opened not so often.  It took me almost one year to find appropriate postdoc position after my PhD. I invest my time and some spare money to local or near international conferences to do social networking, getting career advice and some feedback. I tried to apply for jobs in industry, in small companies, other universities, academic institutions, etc. I got also small grant for short internship. 


Chance favors the prepared mind. Good luck.