Victory leaves Tandy's troops fifth in the RaboDirect PRO12 table, four points behind fourth placed Glasgow who have a game in hand over their Welsh rivals.
And Tandy admits his side need to be nigh-on perfect between now and the end of the season if they are to make the play-offs.
"Credit to the Dragons, the way they defended, pushed the boundaries," said Tandy.
"But ultimately I feel we should have been good enough to rattle up four tries.
"We've just got to keep winning. We don't want to lose games now. Everybody's talking about chasing bonus points. I do think we probably need one, if not two bonus points.
"But first and foremost we've got to get a victory, starting with Zebre."
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Guinness PRO12 Ospreys News
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