Liam Williams responded for Scarlets before the break, substitute Jonathan Evans grabbed a try and a second for wing Evans then put the hosts firmly back in control heading into the final quarter.
A converted try for Sarel Pretorius meant there were just four points in it, but it was not to be for the visitors and Pivac knew his side were lucky to escape with the win.
"It was pleasing to get the five points, but I'm not happy with that first half at all," said Pivac afterwards.
"When we were 20-7 down, the thoughts weren't on the scoreboard, it was more about making sure we somehow got back into the game and more about bringing some physicality, some aggression, some line-speed, which we would have expected to happen, especially playing at home.
"It took John Barclay getting on there to get stuck into them.
"The dose was repeated at half-time and it was pleasing that we played a lot better in the second half.
"I don't know if that (Evans) try came too easily at the start and the boys thought 'here we go, bonus-point win', but we will talk about that on Monday.
"There were individual performances that we were happy with, but it was just really the attitude that we lacked in the first half and that is what we will be addressing, along with some fundamental errors.
"Any side will punish you with that much ball, which is exactly what happened."
Pivac's men moved into seventh place and have a European Champions Cup opener against Sale Sharks at Parc y Scarlets to look forward to next Saturday and Pivac urged his men to refocus before the Premiership side come calling.
"It is a funny feeling," added Pivac. "We are delighted to get five points because other sides in the competition were getting five this weekend and we want to stay in touch with that top six.
"We have got to put the PRO12 behind us now and focus on Sale Sharks next weekend."
Guinness PRO12 Final 2017 Ticket Information: Fans can save up to 20% on selected tickets, and prices start at just €30 adults and €5 child, and be booked via www.ticketmaster.ie. For further information visit http://www.pro12rugby.com/final
Guinness PRO12 Scarlets News
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