The Welsh region, who drew on the opening day of this season to Ulster, can take some consolation from rallying late on to claim a losing bonus point at the Kingspan Stadium.
Scarlets led 13-6 at the interval after a lacklustre first half, but the home side roared out of the traps in the second period to score three tries through Ruan Pienaar, Luke Marshall and Craig Gilroy.
Pienaar also hit two penalties and two conversions, but Kristian Phillips did add a late score for the visitors to claim a valuable losing bonus point and leave Pivac with mixed emotions.
"We were punished for our errors and we didn't exit out of our territory," said Pivac.
"It was important to start well at half time, didn't get the start we wanted conceding tries and falling behind 25-13.
"We came looking for four; the last thing we wanted to do was come away with nothing.
"We dug deep in the last 20 minutes and at the end of the day came away with a vital point. We finished the game strongly - to get that try at the end was pleasing.
"At 25-13 to come away with a point was definitely better than going away with nothing. We would have been very disappointed to come away with nothing after the effort we put in."
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