"There is no right turn or left turn we're going to be making," she said at an open forum with reporters, the New York Times reported Friday.
During a two-day meeting this week, Barra said she informed the company's top brass from around the world that "this is a continuous improvement journey."
"I told the team that there is no destination here ... don't confuse progress with winning," Barra said.
"We want to accelerate," she said.
Her style of leadership is expected to be more open than that of her predecessor Dan Akerson, the Times said.
Akerson, who came from the world of finance, was appointed by the Treasury Department while GM was 61 percent owned by taxpayers due to a massive federal bailout that pulled the automaker out of bankruptcy.
Akerson's take-charge style steered the company through its recovery years while repaying taxpayers.
Barra is an engineer who came up through the ranks in 33 years at GM.
She previously headed the company's global product development.
"Even when you're leading in a segment, that's only for the moment It's a very competitive business and others are looking to surpass you, so you have to continually keep raising the bar for yourself," she told reporters.
Barra tends to shrug off the celebrity status she has been granted because of her gender, the Times said.
"There has been a lot of coverage. But my gender doesn't really factor into my thinking as I come into a room," she said.
"It's going to be an altogether different situation than with Akerson, who was more of a brusque, top-down kind of manager. Mary just has a far deeper understanding of the company and its strengths and weaknesses," said David Cole, former chairman of the Center for Automotive Research.
To Barra's advantage, she is taking over a company that has paid off its debt to the government and matched the industry's average in sales gains in 2013, the Times said.
"I'm a person who looks at the glass as half-full. I also believe if you have a problem you better solve it. Because if you don't solve it, you won't be here or the company won't be here," she said.