Laraine Newman is recalling the moment her daughter Hannah Einbinder revealed she wanted to follow in her footsteps.

In an exclusive conversation with PEOPLE at The Groundling’s 50th Anniversary Alumni Reunion on Oct. 19, the original Saturday Night Live cast member, 72, opened up about how she felt about her daughter’s meteoric rise in comedy.

“I am a genuine, proud mom,” she smiled, before sharing the moment the Hacks star, 29, announced her decision to pursue acting. “It was very late. I mean, she had been an athlete and then she went to Chapman for broadcast journalism and then switched to TV writing. And kids were saying, you’re funny, why don’t you join the improv group? And so that was when she tearfully admitted to me at one point, like the dirty secret, ‘I want to be an actor.'”

Though she admits her daughter was a bit “late in terms of how early a lot of people start,” Newman noted how Einbinder had the chops to go far “right away.” Despite being a comedy legend herself, the actress told PEOPLE why she chooses to not to get too involved in her daughter’s career.

“As a parent, you want to protect your kid, but children perceive advice, unsolicited advice, as criticism,” she explained. “And for my part, my experience is when I try to do that, I pull back a bloody stump. So it’s just, no.”

This isn’t the first time Newman has given her two cents on Einbinder’s performances. While chatting with PEOPLE in September, the comedian revealed that she was initially quite worried about her daughter staring in Hacks, which she has since received three Primetime Emmy Awards nominations and two Golden Globe Awards nominations for.

“It’s thrilling! Everyone on that show is great, and Hannah has risen to the occasion,” she said of watching Einbinder on screen. “She had no acting experience, and as a mother, I was worried, but I didn’t need to be.”

She continued to gush, “Her instincts and delivery are amazing. She even contributes jokes, which is what got her the job.”

Newman then recalled a small moment from Einbinder’s childhood that made her realize her daughter’s writing talent.

“I remember doing homework with her, and she would write these boring sentences, but then come up with something brilliant. I’d think, ‘Why are you holding out on me?’ “

She said, adding, “It’s thrilling to see her shine.”