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Chasing 159 runs to win, the Lions were anchored by Gulam Bodi, who made 64 runs, as they reached their target with three balls to spare for their second victory of the tournament.
"I'm obviously delighted with the result, but it's not something we want to dwell on now," Petersen said.
"We need to focus on the next game and push for the semi-finals.
"Halfway through the game I thought we had given away 15 runs too many, but the batsmen stayed calm after the early loss of wickets."
Petersen paid credit to some of the Lions' batsmen, including veteran Neil McKenzie, who contributed 32 runs in a 93-run stand with Bodi for the third wicket, and Jean Symes, who made 39 not out, and Chris Morris, unbeaten on 12, who compiled an unbroken 44-run partnership for the fourth wicket to carry them home.
"Bodi played exceptionally well with McKenzie, and then the two youngsters finished it off brilliantly or us," the skipper said.
"We knew that we were in with a shout if we managed to get to the last three overs.
"Fortunately for us, they had already used up all their best bowlers by then.
"The guys at the end showed mettle and steel.
"We went through a quiet patch but generally between 10-15 overs it is a sort of dead period when you tend to knock it around, but Gulam never allowed the rate to go beyond 10-11 runs to the over.”
Chennai captain Mahendra Singh Dhoni said his side had a long road ahead of them in the group stages after going down in their second defeat of the competition.
“It is difficult for us to qualify for the semis now but nothing comes easy," Dhoni said.
"We will have to learn from our mistakes and try to come up with some big scores in the next game.”
The Lions play their next match against the Sydney Sixers in Cape Town on Thursday, and Chennai face the Mumbai Indians in Johannesburg on Saturday.
