She made the remarks on Monday before the Senate Judiciary Committee, the panel that will advance or sink her nomination.
If successful, she will be considered by the full Senate as a replacement for retiring Justice Stephen Breyer.
Recent Supreme Court nominations have drawn partisan rancour in the chamber.
If confirmed, Judge Jackson, 51, will be the first black woman justice named to the highest US court.
Announcing her nomination last month, US President Joe Biden, a Democrat, called her "one of the nation's brightest legal minds". It was long past time that a black woman be confirmed to sit on the 233-year-old US Supreme Court, he suggested.
The court plays a key role in American life and is often the final word on highly contentious laws, disputes between states and the federal government, and final appeals to stay executions.
For any Supreme Court justice nomination, the president first chooses his preferred candidate and the Senate then votes to confirm that nominee, which requires a simple majority.
The Senate is currently split 50-50 between Democrats and Republicans, and Vice-President Kamala Harris, a Democrat, gets the deciding vote in the event of a tie.
The Biden administration has indicated it hopes to garner some Republican backing.
While civil rights and liberal advocacy groups have queued up to support the nomination, conservatives say they will closely scrutinise Judge Jackson's judicial philosophy, or how she views and interprets the law. Of particular interest will be her time as a public defender and as vice-chair of the US Sentencing Commission.
In her opening remarks before the Senate Judiciary Committee on Monday, Judge Jackson spoke of her family and her legal mentors and role models.
She clerked for Justice Breyer during the Supreme Court's 1999-2000 term and said the retiring justice exemplified what was needed in the role, the "highest level of skill and integrity, civility, and grace".
Judge Jackson also briefly spoke of her approach to law, saying: "I have been a judge for nearly a decade now, and I take that responsibility and my duty to be independent very seriously.
"I decide cases from a neutral posture. I evaluate the facts, and I interpret and apply the law to the facts of the case before me, without fear or favour, consistent with my judicial oath. "
Chuck Grassley, the committee's top Republican, on Monday promised Judge Jackson a respectful process but said his colleagues would be looking into whether she has imposed her own policy preferences from the bench, which "makes it harder for us to write good laws", he said.
"I'll be looking to see whether Judge Jackson is committed to the Constitution as originally understood," Mr Grassley said.
Democrats are expected to lean heavily on the historic nature of Judge Jackson's selection.
"Your presence here to brave this process will give inspiration to millions who see themselves in you," said Democratic committee chairman Dick Durbin, calling her a "living witness" of what is possible in America.
Her backers will also argue that her resume gives her an informed perspective of the US criminal justice system.
The Washington DC native will not shift the court's current 6-3 conservative majority if she is confirmed.
She currently serves on the influential US Court of Appeals for the DC circuit. Three current Supreme Court justices previously presided on that court.
The jurist has two degrees from Harvard University and once served as editor of the Harvard Law Review.
Mr Biden first promised to nominate a black woman to the top court two years ago while campaigning for the Democratic presidential nomination.
Black women make up about 3% of the federal judiciary, according to data from the Federal Judicial Center, the court system's research arm.
If confirmed, Judge Jackson would only be the third black American to sit on the US Supreme Court, after justices Thurgood Marshall and Clarence Thomas.
Mr Thomas, 73, is the longest-serving Supreme Court associate justice. It emerged on Sunday that he is currently in hospital with an infection, but continues to work in absentia.