The 'Rocket' singer admitted she finds it hard to meet other famous people - which can lead to her accidentally looking rude.
She explained: "I'm always quite starstruck. The first time I met Madonna, I couldn't actually get off the chair to shake her hand. It must have appeared really rude but it was because I was totally gobsmacked that she'd just walked in and made a beeline for me.
"I don't think I actually managed to get any words out; I just sort of froze and grinned inanely."
She added to Time Out magazine: "She's definitely taken the crown as the Queen of Pop. She's the new Madonna, I think. Lady Gaga is passionate about what she does - it's extreme and really good fun. Personally I think the clothes are a lot more interesting than the music. But who knows?
"She's obviously really talented, so it'll be interesting to see where her career goes. I think her success is also to do with timing: we all want something to escape to."
Goldfrapp - which also includes multi-instrumentalist Will Gregory - released their latest album 'Head First' last month.