The win came despite Connacht leading with just 20 minutes to go, Niyi Adeolokun opening the scoring for Pat Lam's side while Jack Carty also kicked a penalty at the Parc y Scarlets
And while Pivac was relieved to get a win which saw Scarlets move up to eighth in the Guinness PRO12 table, the former Fiji coach felt there was still more that could have been done to improve their performance.
"I am very relieved to get the win, it has taken four weeks, a lot longer than we had hoped," Pivac told the South Wales Evening Post.
"Again we left a lot of points out there, there were nine points from goal-kicks in that first half and it would have been nice to have gone in with a bit of a buffer, but that is the story of our season.
"We had to do it the hard way, but I am very happy to get the win.
"When we did play smart, we used territory, used the conditions, tried to keep the penalties down and were able to put pressure on them and score the points that we needed.
"There were still too many mistakes and the boys have spoken about that already, they are obviously very happy in the changing room, but realise they put themselves under a lot of pressure."
While Pivac admitted there were still improvements to be made, the head coach was impressed with how his Scarlets side composed themselves in the closing stages, keeping Connacht without a point to their name in their Guinness PRO12 title defence.
"We are heading in the right direction," he added. "And what I liked was the enthusiasm at the end to deny Connacht a losing bonus point.
"After last week's defeat to Ulster we talked about what is coming up, two out of three games at home and the importance of winning those.
"We are waiting for one of those days when we can relax with 20 minutes to go, but it is not the nature of this competition at the moment."
Guinness PRO12 Scarlets News
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