Ana Maria Archila spoke to ABC News less than an hour after Flake called for the motion in the Senate Judiciary Committee.
But Archila also gives credit to others who she believes helped changed the Arizona senator's mind.
"I feel like everyone [who] has been telling their stories had an impact," she said on "ABC News Live."
"I think people across the country who are telling their stories are changing history.”
Democrats had been calling for the Kavanaugh vote to be delayed to allow for an FBI investigation into accusations that he sexually assaulted Christine Blasey Ford when they were in high school, which he has vehemently denied.
Both Ford and Kavanaugh testified with their respective accounts before the Senate Judiciary Committee Thursday. The committee voted Friday to send Kavanaugh along to the full Senate for a final vote, with 11 for and 10 against, along party lines.
Flake said the motion to delay, which he proposed after meeting with a number of committee members across the aisle, would extend "up to but not more than one week" to allow for an FBI investigation that is "limited in time and scope to the current allegations that are there."
Archila said the proposed delay to allow for an FBI investigation is the "bare minimum" that can be done.
She does not want Kavanaugh on the Supreme Court, she said, but, "I think the country at the very least deserves a process that is more complete."
An activist based in New York, Archila said she is not from Flake's home state of Arizona but still thought she might be able to convince him to change his stance.
"I went to Jeff Flake's office because I think of him as someone who sometimes chooses his conscience over his party," she said of the outgoing Republican.
"I've been trying to understand what moves different senators and today I had my hopes pinned on Senator Flake," she said.
The confrontation between Archila and Flake took place in an elevator as he headed down to the committee hearing Friday morning.
Moments before the confrontation, Flake's office issued a statement announcing that he planned to vote in favor of Kavanaugh's nomination, saying he left Thursday's hearing "with as much doubt as certainty" but felt that the judicial practice allowing a presumption of innocence should be extended to Kavanaugh.
Cameras caught the exchange between Flake and Archila, and she could be heard saying she was a victim of sexual assault.
"What you are doing is allowing someone who actually violating a woman to sit on the Supreme Court. This is not tolerable," the woman, later identified as Archila, told Flake.
When asked about the altercation on “ABC News Live,” Archila said Flake "didn't really want to engage in conversation with us and we weren't really willing to let him go without looking at us."
Archila said she was "so dismayed" by the thought of the vote’s going through in light of Ford's testimony Thursday but now has hope.
"I feel encouraged, kind of a seed of optimism rising inside me that our democracy sometimes works," she added.
"With our actions, we can influence what the senators are doing in Washington.”