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At the end of The End of Evangelion Asuka says

"How disgusting".

Do we know what she meant by that? Is the world that's disgusting now or is she referring to Shinji's actions earlier in the film?

This was addressed in an interview with the film's original (Japanese) voice actor Miyamura Yuuko and the film's producer Ootsuki Toshimichi. She is indeed disgusted by Shinji's actions.

The line was supposed to be "I’d never want to be killed by you of all men, absolutely not!" but after trying it several times, the director decided that it wasn't particularly suiting the scene. He asked the actress what she thought of the situation (learning that Shinji had masturbated over her) and she came up with a new line "kimochi warui" which roughly translates as "I feel sick".

After recording all lines of the movie, I was called to the studio because the final line needed to be revised. Ogata came there too as it was Asuka and Shinji's scene.
Asuka's final line was "Anta nankani korosareru nowa mappira yo!" in the film
scenario. Annno didn't live with my line no matter how many times I tried. Ogata and
I were at a loss how we should play what Annno wanted to express; she even
tried to ride on me and choke me to meet his demand. He must have been pursuing reality.
Concerning the final line we adopted, I'm not sure whether I should say about it in fact.
At last Anno asked me "Miyamura, just imagine you are sleeping in your
bed and a stranger sneaks into your room. He can rape you anytime as you are
asleep but he doesn't. Instead, he masturbates looking at you, when you wake
up and know what he did to you. What do you think you would say?"
I had been thinking he was a strange man, but at that moment I felt disgusting. So
I told him that I thought "Disgusting". And then he sighed and said "... thought as much." He said. " I thought as much."

_{^{Animania Blog: Asuka's final line in the Evangelion movie was Miyamura's idea}}

The American voiceover team (headed by writer/producer/director Amanda Winn-Lee) chose to go with "How disgusting" as an appropriate alternative, after checking with multiple translators.

"Now, there was a lot of controversy as to what this last line should be, and did we do it accurately, and again I asked all three of my translators to look at it [pause] but actually my friend Mari Kamada was the one that provided me with the best explanation of why the line should be how it is, that it was that in the spoken Japanese language there is no word for "I" so that instead of "I feel sick", in all actuality, the character just said "Feel sick" or instead, how we translated it as "How disgusting"."

"But this, once again, huge amounts of research went into making sure
we nailed this absolutely right, that we were absolutely comfortable
with the line we put here because I knew that all the fans who'd seen
the movie before were going to be curious."

_{^{End of Evanglion: DVD Audio Commentary}}