This passage occurs at the very end of the novella. Winterbourne has been thinking of Daisy often since she died. When he sees his aunt, Mrs. Costello, the next summer, he mentions the message that Daisy left for him before she died. Daisy wanted him to know she was not engaged to Mr. Giovanelli. As her mother says at the time Daisy is very ill:

She gave me a message she told me to tell you. She told me to tell you that she never was engaged to that handsome Italian.

Winterbourne says he now understands the message: Daisy wanted him to "esteem" or respect her. At the time she was alive, however, he thought her behavior signaled that she was not a person he needed to "respect."

Of course, saying she "would have appreciated one's esteem" is a cryptic statement, which compels Mrs. Costello to ask if Daisy was signaling she would have returned Mr. Winterbourne's affection had he expressed it. What Mrs. Costello means is: "Are you saying, Winterbourne, that Daisy was telling you she would have accepted a marriage proposal from you?"

Again, we are faced with ambiguity, for Winterbourne doesn't answer. I would take Winterbourne's implied answer to be "yes," but of course, we can't be sure. Winterbourne simply changes the subject and says his aunt was right when she had said he would make a mistake because he was too innocent. Mentioning he made a mistake would again support the idea that Winterbourne felt he should have proposed to Daisy—or that he felt he should have somehow else handled the whole episode differently. We can't be sure how he understands what his mistake was.

The nature of what Winterbourne considers his mistake is never clear: however, he could not have been too deeply attached to Daisy, for the novella ends with the strong suggestion that he is involved in another flirtation.

In sum, a close reading of this ending shows us that this Henry James is communicating through ambiguity and discreet language. Nobody says plainly what they mean, not even the narrator, and one's understanding of the passage depends on the reader's understanding of Winterbourne's character and of the social nuances of the times.

To better understand this part of the story, we must go back and find all the instances that describe Winterbourne's reactions toward Daisy.

We can find two particular times when his attitude towards her is described

It was as if a sudden illumination had been flashed upon the ambiguity of Daisy's behaviour and the riddle had become easy to read. She was a young lady whom a gentleman need no longer be at pains to respect.

Moreover, we find out that Winterbourne elects to merely classify Daisy under some proper category to excuse his inability to accept her unique qualities. 

She was very unsophisticated; she was only a pretty American flirt. Winterbourne was almost grateful for having found a formula that applied to Miss Daisy Miller.

This being said, we see how Winterbourne's cold nature is reflected properly in the name of his character, and in his interactions with Daisy. As a man who cannot understand how a woman could be naturally open-minded and outspoken, he basically drowns his emotions toward Daisy in favor of a more traditional view of women.

Clearly, Daisy does not help matters with her insecure and immature behavior. We can only excuse it because, as readers, we know that all she wants is to get the cold and calculating Winterbourne to "throw her a bone" and show some interest in her. 

However, after Daisy dies, we witness that Daisy had made a final attempt to redeem himself to him. When Winterbourne reads the letter, he understands that he should have given himself an opportunity to understand Daisy better. She was not a bad person, but an inexperienced coquette. Yet, he cannot help his nature, and continued with life as usual in Geneva.