Saturday's four point loss leaves Tullamore seventh in the standings.
Tullamore continued their inconsistent form in Division 2C of the All Ireland League last time out against Bruff.
The Limerick club left Spollanstown with four points thanks to a 14-10 victory over the home side on Saturday.
Darin Classin's side can add just a fourth win to their league tally this weekend when they face Bangor in Uprichard Park.
The action in County Down will kick off at 2.30pm.
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