Kirke shares Rafella and Memphis with her ex husband, lawyer Michael Mosberg.
The actress and artist is now dating Australian musician Alex Cameron.
Over on Twitter, fans admired the star's honesty, adding that it was refreshing to see a high-profile mother acknowledging their caregiver.
"Props to her for honesty. I too hate playing and unfortunately for my kids, they can tell!," one said.
Another agreed: "I do not like playing with my kids! I like talking with my kids, reading with my kids, eating with my kids, napping with my kids. Unfortunately I do not have a nanny to do that for me ha ha."
But not everyone was a fan of her candour.
"She can't stand playing with her children, what a thing to say!," one follower posted.
Another wrote: "This makes me feel so icky. I can't imagine refusing to partake in something so important to my child. I hope it's not completely serious."
"Yeesh that's gonna be tough for a kid to read someday," one more offered.
Others were quick to point out other Hollywood women who had honoured their nannies in the past, including Busy Phillips, Tina Fey, Amy Poehler and Kelly Clarkson, news.com.au reports.
"Poehler and Fey had their nannies in an SNL skit once. But verrrrry rare," one said.
34-year-old Kirke split from her husband of seven years in 2017, blaming her acting career for the breakdown of her marriage.
Kirke told ES magazine that she started to analyse things differently after her high school friend Lena Dunham cast her as Jessa Johansson in Girls.
"I got divorced, and I attribute that to acting. And just asking myself, 'Is this really me?' So much of my life has been about reaction, just following the flow rather than making a strong choice," she said.
"In acting you are always asking yourself why you do things, why you make the choices you make. Everything means something. And so then you start looking at your own life in that way. I've learnt a lot more about myself and started to figure out what I really want," she said.
