Maybe she didn't like it. It's rated G, I started watching anime since I was 5 so I don't know if it's the different culture or what. Try showing her Totoro, it's a very good kids film, it's magical, it's about creatures, it's about children, all stuff that three-year-olds are interested in.
But I wouldn't show a young child the more mature stuff such as NAusicaa, Princess Mononoke, Spirited Away etc., she might not appreciate them.
I hope that there is an Evangelion video game where you can beat Asuka up!

My 4 year old son loves Ponyo. Though he said that he wants to smash the tv to keep her from turning back into a fish. o.O

It really depends on what the child is interested in. We just watched Ponyo for the first time today, and my two-year-old daughter is already asking to watch it again. I think Totoro is a really good starter film, too. She loves that, and we used it as a tool to try to explain that she will be a sister soon, just like the girls in the movie. She also likes Spirited Away, but she wasn't very interested in Castle in the Sky. She seems to be more interested in the movies with younger children.

I think it's worth trying Ghiblis from a young age, maybe give Totoro a go (though a year and half after your post I guess things have changed!). It depends what the kids are used to watching (short/long, fast/slow) and what mood they're in etc. My son and daughter each loved Totoro by the age of two. The daughter then went crazy for Spirited Away and it's still her favourite film now at 5. The boy is a little younger and doesn't seem to get the slightly more sophisticated films yet. He's 2 and a bit and if you catch him in the right mood he'll sit through Ponyo but not stuff like Laputa, Nausicaa, Spiritied Away etc. I still think Totoro is the best introduction to Ghibli but, again, it depends what they're used to. The other Miyazaki thing they both adored from very young is Panda Kopanda.

My daughter liked it at 5 and loves it at 7. She also really loves My neighbor Totoro. At 7.5 yrs she and I are watching every Miyazaki film and she loves all but Princess Mononoke - too soon for that.

My 3 year old twins are watching Ponyo right now and are completely entranced by it. So am I. Each child is different. Try again in a few months.

This IS the most kid friendly
Miyazaki
flick. If she wasn't into it, you'll just have to wait until she turns 12 to show her the PG animes.

I suggest from 6 onwards really. I remembered Nausicca Valley of the Wind for one of the visual images in it from when I was age 5 or something but I, honestly, was not interested in the story. I think as a kid I could tell that it was too complicated and as a child, I did not just want to sit down and watch it. I wanted to play. In other words, I found the story slow.
Ponyo is the most simplest of Ghibli films. I would suggest try from age 6 onwards.

Try again in a year or two.