The comments were an elaboration of Ginsburg's belief that the Supreme Court should have nine members.
Last May, she told an audience in New York: "Eight, as you know, is not a good number for a multi-member court."
The 83-year-old justice called Scalia's sudden passing the most "momentous occurrence" of last term, which included cases on abortion, affirmative action and immigration.
"His absence will be felt for many terms ahead," she said.
Wednesday's event was a wide-ranging conversation before students at Georgetown Law, where she dispensed advice, spoke about her trail-blazing cases as an advocate concerning gender discrimination, and addressed court cases she felt should be reversed.
Ginsburg was greeted by a standing ovation from the students, many who refer to her by her nickname the "Notorious RBG."
As she walked the students through the cases she argued as a young lawyer to bring down arbitrary gender lines, she recalled her own battles with discrimination. When she sought a job and "employers were totally up front in saying, 'We don't want any lady lawyers in the shop.' "
Her efforts in those days were to battle "variants of the same theme" that the man is the dominant partner and that the woman's domain is "home and children."
"We wanted to break down the stereotypical view of the world," she said.
The justice said that it was "beyond wonderful" to be part of a successful movement as a young lawyer when the law caught up with the experiences of many people.
Ginsburg -- who is about to begin her 23rd term on the court -- allowed that the most challenging part of being a justice (a job she called the hardest job she ever had) is the "sheer stamina" it takes.
She has shown no signs of slowing down, however, and next month she will take the bench for a term that will include cases on the death penalty, redistricting, disability rights and racial discrimination in housing among other issues.
The justices might also agree to hear a case concerning transgender rights. Also still pending is a long-shot request from the Obama administration to re-hear a case concerning the President's controversial immigration actions. Last term, the court deadlocked 4-4 in the case and in doing so affirmed a lower court opinion that blocked the programs.
The court has been unusually busy in late August and September, dealing with emergency petitions concerning voting rights issues in key election states such as North Carolina and Ohio. Because the court is closely divided on many voting rights issues, the possibility of 4-4 splits means that some lower court opinions remain the last word on the subject.
In her talk, Ginsburg did not delve deeply into last term's cases, but if a Democratic president succeeds in nominating the next Supreme Court justice, the court will take a turn to the left. Recent cases she thinks should have come out the other way include the 2010 campaign finance case, Citizens United, as well as Shelby County, a 2012 case that struck down a key provision of the Voting Rights Act.
She also went out of her way to mention a dissent written by Justice Stephen Breyer she called impressive on why "the death penalty is cruel and unusual punishment."
Even with only eight justices, by and large last term was a good one for liberals on the bench. The court struck down a Texas abortion law that critics said was one of the most strict nationwide, and it upheld the race-conscious admissions policy at the University of Texas. Justice Anthony Kennedy's vote was key in those cases.
Ginsburg was not asked and she did not offer any comments concerning Republican Donald Trump's presidential candidacy.
She caused a firestorm at the beginning of the summer for comments she made to media outlets concerning the businessman. She told Joan Biskupic,
CNN's legal analyst and Supreme Court biographer, for instance, "he is a faker."
"He has no consistency about him. He says whatever comes into his head at the moment. He really has an ego ... How has he gotten away with not turning over his tax returns?" she said.
Ginsburg later issued a written statement saying she regretted the remarks she had made to the press.
"On reflection, my recent remarks in response to press inquiries were ill-advised and I regret making them," Ginsburg said in the statement
. "Judges should avoid commenting on a candidate for public office. In the future I will be more circumspect."