Falco, who plays the lead role, explained that she often doesn't realise how many people watch the show.
"The weirdest thing was two summers ago," she told The Guardian. "I'm in The Hamptons, bouncing my baby in a swimming pool, and there's an aeroplane going by with a banner with Nurse Jackie on it.
"It was just too bizarre. We go and do our job and go home and you forget that it's being recorded and millions of people are seeing it. That piece of it is something I don't think about so much. Until somebody comes at me with that kind of grin as if I'm something other than human."
Falco revealed that she managed to avoid the critical acclaim that surrounded her previous show The Sopranos as well.
"My mum would call and say, 'Oh, I was reading on a website', and I'd go, 'Mum? I can't go there'," she explained. "It wasn't until it ended that I became more aware of just what it was and what it meant to people. It's just hugely flattering."
Falco also admitted that she sometimes gets frustrated with Jackie on Nurse Jackie.
"I think I'm tougher [than her]," she said. "And my toughness was hard-won so I can stand by everything I say and do. I get impatient with her denial - I just want to say, 'You've got a marriage, kids at stake, just get it together, enough already!'"
The third season of Nurse Jackie is currently airing in the UK on Tuesdays at 10pm on Sky Atlantic.
Watch a clip from the next episode of Nurse Jackie below: