finish ?

I need help. I'm reading Daisy Miller by Henry James and don't know what finish exactly means in this novel.
Here is the part of the novel that have the word finish in it.

He had a great relish for feminine beauty; he was addicted to observing and analysing it; and as regards this young lady's face he made several observations. It was not at all insipid, but it was not exactly expressive; and though it was eminently delicate, Winterbourne mentally acused it - very forgivingly - of want of finish.

I asked my teacher it might be make-up. His reply was 'You're degrading Winterbourne's character.' HaHaHa

Perhaps he is saying that her face was a little bland, not ugly but not exceptionally good looking either.

Thanks, but this novel says she is a pretty girl.

It goes like this : This pretty american girl, however, on hearing Winterbourne's observations, simply glanced at him. ~ They were wonderfully pretty eyes; and indeed, Winterbourne had not seen for a long time anything prettier than his fair countrywoman's various features - her complexion, her nose, her ears, her teeth.

The only other thing I can think of, other than Make-up which would have been my first guess too, is that she keeps her face neutral. That is to say she doesn't allow herself to express her emotions but instead keeps her features schooled.

Thanks a lot!