Pivac’s Wales sealed a bonus-point success over Scotland but only by the narrowest of margins thanks to two tries from man of the match Louis Rees-Zammit.
Liam Williams and Wyn Jones also scored as Scotland were reduced to 14 men following prop Zander Fagerson’s red card. In the end, Wales were 24-25 winners.
“It’s a very pleasing start, but I think it was evident to everyone that it wasn’t the complete performance,” said head coach Pivac.
“Alun Wyn Jones has spoken about that in the changing room and we’ll address our game in the next couple of weeks.
“It’s only round two of the tournament and we’d expect to be improving every time we take the field.
“At 17-3 down, it wasn’t going to script but the players regathered their thoughts, the leadership on the field was good, and we came away with that score before half time.
“That was vital for us going into the changing room. The players reacted very well after half time, the replacements made an impact, and it was very nice to get the result at the end.”
It’s a very pleasing start, but I think it was evident to everyone there that it wasn’t the complete performance
Fagerson collided with Wales prop Wyn Jones in the second half.
Pivac added: “There is nothing else the officials can do, really. The laws are pretty clear cut now.
“It’s one of those unfortunate things and players are going to have to look very carefully at how they enter those rucks.”
On Rees-Zammit, Pivac said: “He was exciting with the ball, wasn’t he? He took his opportunities very well. He’s still got work to do on his game without the ball, and that’s the exciting thing.
“He’s going to be a very exciting player for us going forward.”
Scotland captain Stuart Hogg scored twice after a Darcy Graham effort, but they fell just short and couldn’t back-up their win over England.
Wales captain Alun Wyn Jones added: “We’re well aware there are massive improvements to make.
“You can’t give a team two tries, but I’m pleased with the resilience, character and pride in the jersey we’re still showing. What you’re seeing as well is a product of the experimentation from the Autumn Nations Cup and the hurt we took.
“Irrelevant of the advantage, I’d like to think we were in the ascendancy before the card.
“We’re aware England had a good win and are back on track. We’ll be back at Principality so we’ll regroup and improve on the parts we need to.”
We’re aware England had a good win and are back on track. We’ll be back at Principality so we’ll regroup and improve on the parts we need to.
Gloucester wing Rees-Zammit, just 20, said: “I’m most definitely smiling. We’ve come a long way from the very start of the last Six Nations campaign. We’ve worked so hard in the past few weeks in training.
“It’s hard to come up here and get a win. It wasn’t a pretty one, but thank God we did it.”
On his second try which saw him kick ahead and collect to score, Rees-Zammit added: “I just tried to use my gas and get on the outside. I saw there was no cover in the back field so I put a kick over the full-back and I got the bounce. It came straight into my hands.
“I’m thoroughly enjoying it here. I’ve settled in really well with this team and they’re all helping me.
“I’m loving being here and playing on this stage.”
Alun Wyn Jones added: “Louis has been playing well for Gloucester in the Premiership. I’d heard a lot about him and seen a lot of highlights of him. Hopefully this is just the tip of the iceberg.
“I don’t want to heap the pressure on him, I want him to continue in the similar vein.”
I’m loving being here and playing on this stage