"Well, this is a very intense moment," she told ET's Nischelle Turner just before she presented the award.
The former Alias star further discussed how she talks about the culture of abuse with her own children, Samuel, 6, Seraphina, 9, and Violet, 12.
"It's so important to find a way to talk to our kids and help them know that they're always safe coming to us, they can tell you anything, anything," Garner shared. "I don't know, I bumbled my way through [a talk about it] the way anyone would, but I think it's just really important to keep the conversation going."
When Garner took the stage minutes later she called what the women went through "a nightmare." Following her speech, Aly Raisman, Sarah Klein and Tiffany Thomas Lopez opened up about their own experiences with the other 138 women surrounding them on stage.
Jennifer Garner upon introducing the story of the Larry Nassar survivors who are receiving this year's Arthur Ashe Courage award: "It's a story about what can happen in sports…when the dream of being an athlete turns into a nightmare." https://t.co/T3gtmmd6PF#ESPYSpic.twitter.com/A8cbNFR3bZ
Before the ESPY awards, Garner was working hard to get in shape for her upcoming action movie, Peppermint, which is due out in September.
"You know I was doing what I had been doing before, we just upped the intensity and we upped the times a day that I worked out," she revealed. "I was working out with Body by Simone's Simone De La Rue and we kept dancing. We danced our way through it."
Despite growing up dancing, Garner revealed that she "wouldn't call myself an athlete."
"I cannot throw or catch a ball to save my life," Garner joked. "I live in fear that somebody is going to be like,' here, catch' and I'll duck."