Tyrone suffered a 2-point defeat to Louth, leaving them level with Kildare but just one point above Cavan in the drop zone.
With Canavan departing for Australia, O'Rourke faces a difficult task ahead of Saturday's home clash against Offaly.
Tyrone's Canavan a big loss in relegation fight
Tyrone manager Malachy O'Rourke admits Darragh Canavan will be a major absence as the Red Hands fight to avoid relegation from Division Two.