Tubridy asked Farrow if the first time she met her first husband Frank Sinatra, when she was just 19, "stood out" for her.
The actress was taken aback and replied: "Does it stand out? Oh my God, yeah of course."
The self-confessed 'young fogey' then wanted to know if Farrow (67) could "recall the shoot" for her famous film Rosemary's Baby.
The Oscar-nominated star was bewildered by Tubridy's line of questioning.
"All this recall business. I know I'm old, but I'm not that old," she said.
"I'm likely to remember these things like a marriage or a film."
Tubridy then attempted to explain that he had asked it in such a way because she had such an interesting life and was wondering if "all the memories mix up in one go".
She replied that her memory was fine, so far. "Not yet, I'm sure they will though," she said.
The interview took a turn for the worse when Ryan clumsily asked why she had decided to adopt so many children.
The Unicef ambassador sarcastically replied that perhaps she needed some therapist time.
"We'll lie down on the couch and we'll just figure it out together," she said.
And Tubridy was most uncomfortable bringing up the subject of her former partner Woody Allen (76) who is now married to her adopted daughter Soon-Yi Previn (41).
Tubridy asked the actress if she is in contact with the film director.
"Every day. What's the matter with you anyway? Jesus," she said .
Fans of the blonde star took to online message boards to criticise how the interview was handled.
Later, the Unicef Goodwill Ambassador responded to comments on social networking sites and admitted that she was "very nervous" and replied to one follower: "He's not very gracious."