Open the admin link and click on the top menu 'More' and then on 'Export to Excel'.
Open the Excel file and click the 'Invitees' tab (the file includes two spreadsheets: the poll and the list of invitees). You can copy and paste the email addresses from there.
Furthermore you can duplicate polls and reuse the same list of invitees if you like (More -> Duplicate poll).
If you have an active Premium subscription, you can also see the list of invitees in the poll table. The email addresses are listed below the participations, but only if the invitees did not yet participate.
If by chance you do not see the list of invitees you can try reloading the page.
If you invited yourself (with your own e-mail application), Doodle can not tell you who you invited to the poll. In this case you have to search for the e-mail. The easiest way to find your e-mail is to search for the poll link. The e-mail header (To / Cc / Bcc) of the e-mail reveals all used e-mail addresses of your invitees.