Liv, 11, had been impressed to think her mum was appearing opposite Hunger Games star Hemsworth in forthcoming film Non-Stop.
But 53-year-old Moore tells tonight's Graham Norton Show on BBC1 that the youngster had mistaken the Irish screen star Neeson for the Australian actor.
She said: "I told her I spent the day with Liam and she said it sounded like fun so I sent her a picture and she said, 'Who's that?' I said, 'Liam Neeson' and she replied, 'No, Liam Hemsworth!' who's Liam Neeson?'"
Moore also said she snubbed a royal invitation shortly after receiving British citizenship at a ceremony in Los Angeles, and instead headed to Disneyland.
She said: "That was the day there was a garden party for William and Kate. As an American I couldn't go, but as soon as I was sworn in I had an invitation. Being an American at heart, I thanked them for the invite but went to Disneyland instead."
Four-time Oscar nominee Moore also told presenter Norton how she is on the receiving end of back-handed compliments.
"People think they are saying something really nice when they say things like 'you're so little, I thought you were bigger', or they say 'you're prettier than I thought.' They mean well but what do you say? Thank you, I think."
The interview is screened tonight at 10.35pm on BBC1.