Tandy shared his delight with his side's fine defensive display and was pleased with the discipline his players showed as Scarlets lost Aled Thomas to the sin bin and Gareth Owen and Rob McCusker to red cards in a bad-tempered ending.
But he is urging the Welsh region to keep up their form when they visit second-bottom Newport Gwent Dragons on New Year's Eve before welcoming 12th-placed Zebre to the Liberty next Friday.
"Our all-round team performance was outstanding," said Tandy. "I thought our discipline was outstanding in defence and we did not give away a lot of penalties.
"We know the Scarlets have a lot of outstanding attack threats but we are comfortable without the ball and have some good defenders.
"We spoke before the game that we didn't want to give cheap penalties away, and we worked hard on that throughout the week. We pride ourselves on our defence and our discipline in and around the contact area was very good.
"The group want to recover because they know we have a massive game against the Dragons on New Year's Eve. Zebre are bottom of the table, but if we can get anywhere near the support we had (against Ospreys) for that one, fingers crossed it will be a decent Christmas.
"We don't want the bubble to burst. We have never fared well at the Dragons and we want to put that right. We'll come back here and we'll look for at least four points against Zebre and then we are back in the Heineken Cup."
Tandy was also full of praise for influential fly-half Biggar and scrum-half Kahn Fotuali'i, who grabbed a try of his own.
"Kahn understands the way we want to play and he and Biggar are driving things at the moment," he said.
"Kahn is world class for us at the minute, so it is great for us."
Tandy's mood was in contrast to Scarlets head coach Simon Easterby, who was dismissive of his team's performance but conceded the lack of discipline was disappointing.
"I saw that performance coming because we have been poor for the last four or five weeks," he said.
"We played on a poor pitch in Cardiff last Friday where we managed to come away with a result.
"We are not good enough at the moment. We might be in second but that can soon change. We are not playing like a team in second spot in the table.
"There is a huge amount of work that needs to be put in for the New Year."
And the former Ireland flanker was equally disappointed to finish the game three players light.
"I will have to look back at the game and the individual incidents to give a better view," he said.
"But it was disappointing to see so many players walk off the pitch from either a red or yellow card. That has to be a concern."
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