If you invited your participants via Doodle, open the admin link and click "Contact invitees". You will see all invitees (section “E-mail addresses”).
If you invited your participants manually, Doodle can't tell you who you invited. In this case you have to search for the E-mail you sent to invite everyone. The easiest way to find your mail is to search for the participation link which is stated in the admin-tab of your poll. Open the E-mail. In the header (To/Cc/Bcc) you see all E-mail addresses of your invitees.