But despite a disappointing defeat on home soil they managed to hang on to second place in the Celtic League, even after the Ospreys scavenged late efforts to deny them a bonus point.
It was a lethargic effort lacking in continuity from Ulster, who were in the strange position of having eight of their starting side with the Ireland squad.
Ospreys, who were handed the only try of the game, have had more practice within their squad of losing frontline players.
Ulster were regularly in a state of flux, even though they had territorial advantage for most of a game in which errors were commonplace.
With a sodden pitch and the wind at their tails, they attempted to turn the screw from the first whistle, but a first chance passed by when Paul Steinmetz saw a 48-metre penalty scrape past the upright.
The Ospreys took the lead with their first venture into Ulster territory when Shaun Connor popped over a simple penalty in the 13th minute.
Ulster continued to press and were finally rewarded after some stout forward play when Steinmetz levelled with a penalty but that was matched by another effort by Connor, who ended the half with a third penalty.
In the second half, Ulster did keep up the pressure on the Ospreys, camping in their half, and Steinmetz levelled again with his third shot at goal.
But it was the Ospreys who scored the first try of the night after 58 minutes through a comedy of errors with Campbell Feather unable to kill a loose ball and presenting scrum-half Jason Spice with an easy touchdown.
Ulster could not force their way through the Ospreys blanket defence and while Steinmetz clawed back the lead with another penalty in the 61st minute, another Ulster error allowed Connor to knock over his fourth penalty with two minutes remaining.
Just for good measure Connor denied Ulster a bonus point with a snap drop goal in injury-time.
ULSTER: B Cunningham; J Topping, K Maggs, P Steinmetz, A Maxwell; P Wallace (Larkin 71), I Boss; J Fitzpatrick, N Brady, B Young (R Moore 24), J Harrison, capt, R Caldwell (H Head 69), C Feather (S Ferris 62), N McMillan, R Wilson.
OSPREYS: A Cashmore; R Mustoe, A Bishop, L Davies; A Brew, S Connor, J Spice; P Jones, B Williams, capt, A Millward, A Newman, I Evans, J Bater, S Tandy (R Pugh 68), L Beech.
Referee: Iain Heard (SRU).