And it could have been even worse for Pivac's men had Tom Heathcote's penalty in the 80th minute not fallen just short of giving the Scots a memorable victory.
The Welsh side dominated the first-half as Harry Robinson crashed over after just 40 seconds before Liam Williams dotted down and Welsh international fly-half Rhys Priestland also kicked ten points.
But converted tries from Tim Visser and Phil Burleigh and a pair of penalties from Heathcote ensured that Edinburgh stole a share of the spoils, and Pivac admits that his Scarlets side must perform better under pressure.
"It was disappointing that we weren't able to get the four points," he said.
"We've been starting our games well and a try in the first 40 seconds is a great way to get underway but we didn't capitalise on the opportunities we created.
"We allowed Edinburgh back into the game and gave away too many penalties in the second half.
"In a tight game like that, it's all about field position and staying in the arm wrestle. We need to be putting pressure on the opposition so that they're the ones giving away the penalties.
"We felt at half time that it was ours to win - as it was ours to lose. We did enough in the first half and if we'd have scored that other try it might well have been a different game.
"We'll be working on decision making under pressure this week. We're heading home next weekend and looking forward to playing in front of a passionate Scarlets crowd."
Click here for the best images from Edinburgh's 20-20 draw with Scarlets.
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