With the wind at their backs Liam Williams' try and Rhys Priestland's conversion had given Scarlets a 7-5 lead at the turn around.
However, converted second-half tries from Peter Murchie and DTH Van der Merwe and a Finn Russell penalty saw Glasgow score 17 unanswered points.
That subjected the Welsh province to their sixth GUINNESS PRO12 defeat of the season and left Pivac frustrated.
"It was a 20-point wind out there, as Glasgow proved scoring 17 points in the second half, to turn the first half around to a two-point lead wasn't enough," he said.
"Seven penalties went against us in the first half and we didn't use the wind as frequently as we should have. We tried to play too much rugby in our own half.
"With Glasgow having a high percentage of the possession it meant that we spent too much time in our own half.
"We didn't take advantage of the possession that we did have, gave away too many penalties and Glasgow put too much pressure on us with the wind advantage."
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