Heading to Rodney Parade with four straight league wins to their name, the Dragons prevented Ulster from making it five and going top of the table with a 26-22 victory.
Ulster did, however, move up to second courtesy of their losing bonus point and Munster's defeat to the Ospreys.
But for Doak, failure to make it four wins in as many weekends has left them with a lot to do in order to secure a home semi-final.
"We knew it was four tough games for us and we knew we really had to get four wins," he told the Belfast Telegraph.
"That would have set us up nicely but now we've got to make sure that we're error free and disciplined for the rest of the season.
"Coming away from home is always difficult, but to get a point and still be in the top four, and in second position, is key for us and we've got to make sure that we stay there for the rest of the games."
A Craig Gilroy double and a late score from Ross Adair threatened to hand Ulster a battling victory in Wales but it was not to be.
However, a trio of Dragons tries in the second half - from Rhys Buckley, Jonathan Evans and Carl Meyer - did the damage.
"We didn't kick particularly well and in hindsight when we look at the pack we had out they should have been a little bit more dominant for us," added Doak. "But just across the board we didn't use the ball wisely.
"We let them run at us and that boils down to the energy and will and we just didn't have that."
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