Price and Jamie Ritchie led their team to a 10-try win over Tonga.
The Scots scored 10 tries in what was a hugely encouraging display from a team missing some big players and featuring four debutants in the starting XV. Kyle Steyn was the star of the show as he became the first Scottish player ever to score four tries in a match at Murrayfield.
He said: “All week we trained well, with good tempo and pace, and it was good to see us take that on to the field and get our rewards for it.
“You can always take positives and negatives from every game and a big thing we took away from Saturday was that our discipline wasn’t good enough in terms of the amount of penalties we gave away in the areas that we did against Tonga.
“If we do that in a game where the score is a bit closer, that could cost us. Defensively, we maybe need to get our width a bit better because if the opposition execution had been slightly higher, we’d have got stung a couple of times.
“The attack was pretty good at times but there are always things to improve. We’ll have to play better against a higher-ranked team, that’s for sure.
“In terms of world rankings and results, Australia will be a tougher test. We’ll have to get better. We have areas where we know we can get better for next week and moving forward.
“We know what a big test it’s going to be. But we’ll have a full complement in the squad with everyone available for selection, and a full BT Murrayfield. If you can’t get excited about that, you’re in the wrong job.”
Price, 28, was proud to lead Scotland for the first time.
The Glasgow scrum-half said: “I loved the captaincy. It was a very special moment for me being stood in the tunnel, up the front, and all I could see was the pitch and the opposite stand with all the people there.
“It really sunk in at that point what was about to happen. It was an incredibly proud moment for myself and my family in the crowd.
“I think the division of duties between me and Jamie worked well. It was quite a natural split in terms of one of us being a forward and the other a back.”