The Blue Toon’s 4-3 success at Balmoor was their first victory since they beat the same opponents at Dumbarton on December 18.
But while he was delighted with the win, the Peterhead gaffer was less than happy with his players’ second-half display.
After leading 3-0 at half-time against a Dumbarton side reduced to 10 men before the interval, they allowed the Sons to pull two back.
A second Dumbarton red card and a fourth Peterhead goal then seemed to settle the outcome but Dumbarton still pulled another goal back in stoppage time to ensure an anxious finale.
McInally has praised his players in defeat on a number of occasions this season, but the boot was on the other foot after Saturday’s encounter.
He said: “We've just went through them there. That's the poorest 45 we've played in a long time. Not that I'll dwell on it too much because the first 45 was really good.
"I know the weather played a part in the game, we knew it would do, but we were slack in the second half.
"To give Dumbarton some credit they played in a kamikaze way in the second half where they were either going to get thrashed or get back in the game."
McInally described the goals his side lost as a comedy of errors and conceded that a recent defeats could have contributed to Peterhead fragility at the back.
He said: “What's probably going into the their minds is the same as is going into my mind, is it going to happen again?
"But you need to be bigger and better than that.
"I wouldn't have minded if we were under pressure but they weren't really putting us under pressure.
"We were in great positions. With a bit of care we could have scored a lot of goals.
"They just played to get back in the game, and credit to their manager for being as brave as that, but we should have taken advantage of that situation and we didn't.
"I'm delighted with the result but not the second-half performance."
Peterhead host Queen’s Park tonight (Tuesday) followed by a trip to Cove Rangers on Saturday