I fail to see how the OP can blame Orbitz for this. The OP should have checked the email-adr. before completing the reservation.
Anyway, even without a confirmation email it should have been possible to trace the reservation by speaking to Orbitz CS (or calling the hotel to get the Orbitz reference No). Knowing that a reservation was made but doing nothing when the need to cancel arises (and a likely no-show at the hotel) because no conf. email was received, is not a reasonable way to deal with this situation.