The Hollywood legend has joined the cast of the hit ITV show as Martha Levinson, the wealthy mother of Lady Grantham (Elizabeth McGovern) - whose American attitude is set to clash with the formidable Dowager Countess, played by Dame Maggie Smith.
Shirley told the Daily Telegraph: "I've been watching the series on TV and I love it. But I'm still not quite sure why it is such a big hit.
"Here as well as in the UK. I knew I loved it but I didn't know all these other people were looking at it. I found it very encouraging about the intelligence of the audience, to tell you the truth. Yet I'm asking myself what is it about this show that is proving so irresistible?"
The 77-year-old star of The Apartment thinks one reason could be that the opulent period drama offers viewers an escape from the reality of the current recession.
She said: "When times are bad, people like to lose themselves in the sheer glamour of another period: beautiful wardrobes, magnificent meals served in elegant settings. It's brilliantly done, great writing and fabulous costumes and all that - and certainly the ambience of that time and age is appealing."
And she is looking forward to working with Dame Maggie.
Shirley said: "When my agent called and asked: 'Do you want to go head to head with Maggie Smith in the British series?' I just chuckled.
"It's not going to be a problem, I'm certain Maggie and I will get along just wonderfully. Intimidating? Certainly not!
"Maggie's got nothing to fear from me, and I'm just thrilled at the prospect of working with her. I love her to death."