The Northern Irishman have not conceded a try in three consecutive league matches - the latest a 23-6 win over Newport Gwent Dragons - and have shipped just 82 points in seven games so far.
Following the forthcoming international break, third-placed Ulster take on league leaders Ospreys at Kingspan Stadium.
And Doak hopes another shut-out can close the gap at the top as they bid to win a first league title since 2006.
"This was the third league game we haven't conceded, so from that point of view it's very pleasing and it keeps us there or thereabouts," Doak told the Belfast Telegraph.
"The first half was very good. The tempo was good in the conditions, but we just didn't have the accuracy in the second half to really finish things off.
"The conditions were difficult, but it's disappointing to create opportunities and not take them.
"If we had been a bit more accurate in the second half we might have come out with five points but we're happy to get the win on the back of two difficult European games."
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