The Durban side easily overcame the Bulls 31-16 at Kings Park, taking a four-try bonus point along the way, and in the process sent out a strong message to the rest of the competition.
“I think there definitely is a feeling that we can get a lot better,” Lambie said.
“Our shape can improve, our work off the ball can improve and there are other aspects too.
“We don’t feel like we played that much or that well, which is an encouraging thing and we will be looking to improve throughout this week and put that into practice.”
The 23-year-old played down the pre-tournament “favourites” tag that has been attached to the Sharks, who are at the start of a new period following the appointment of ex-Bok boss Jake White as the director of rugby at the end of the last term.
“We try not make that add any additional pressure to the whole situation,” he said.
“I think we have to take it one week at a time. It’s all about the processes. If anything, I think it should instil more confidence amongst the group.”
Lambie has been given the full backing of White to play in the number 10 jersey this season as he bids to become the established flyhalf in the national set-up under Heyneke Meyer.
He was used in different positions by the Springboks in recent years and his new mentor at the Sharks has made no secret of his desire to establish the player in the pivot role.
Lambie made a solid enough start on Saturday when he scored 16 points, including landing the bonus-point try after the final whistle.
“It was a decent start,” he explained.
“I missed a couple of opportunities but it was still pretty good. I am working hard and we’ll keep going and keep enjoying it.”
He also revealed how White wanted him to command play from the position.
“He wants me to take charge… to control and direct the forwards,” Lambie said.
He said that if he could get better with that every week, the team would be in a good space.
“There is an outline of how Jake wants us to play, something that’s necessary at this level, but he’s big on making us react to what’s in front of us,” Lambie said.
“That means you need to know when is the right time to get the ball in your hands, to have a go and when to kick.
“We do have licence to play what’s in front of us and to attack the space.”
The Sharks, who had no injuries to report after the weekend win, face New Zealand outfit the Hurricanes in Durban on Saturday.