Take a look at this passage, from Section 3, when Dexter finally nabs a date with Judy:
During dinner [Judy] slipped into a moody depression which gave Dexter a feeling of uneasiness. Whatever petulance she uttered in her throaty voice worried him. Whatever she smiled at — at him, at a chicken liver, at nothing — it disturbed him that her smile could have no root in mirth, or even in amusement. (3.7)
The reason for Judy's sadness matters less than Dexter's response to it (though it does tell us something about her character). He can see that something is wrong. But Dexter cannot for the life of him figure out what it is. The problem is, Dexter can look at Judy all day long. He just doesn't understand her. That, in and of itself, is pretty darn sad. He longs for a Judy he'll never have.
The language of the passage makes us feel like we don't actually know what's going on ("uneasiness," "worried," "disturbed"). Fitzgerald's use of all of these anxious words makes us anxious as readers. And we'd bet that was intentional. The tone in this passage helps reinforce the idea that Judy is to be longed for, but never to be had. She's a dream, but she is also an unreachable goal.
How about one more example, with an equally wistful tone:
The dream was gone. Something had been taken from him. In a sort of panic he pushed the palms of his hands into his eyes and tried to bring up a picture of […]her mouth damp to his kisses and her eyes plaintive with melancholy and her freshness like new fine linen in the morning. Why, these things were no longer in the world! They had existed and they existed no longer. (6.34)
What's going on here? Check out the repeated words of loss: "gone," "taken," "no longer." The narrator practically beats us over the head with it: Dexter has lost something – his dream, to be precise. And when he realizes this, he longs for what he's lost downright desperately. All he has now are memories, of a woman he never really had, and of dreams he never really achieved.