When you're a kid in Ember, your life isn't all fun and games (well, except for the parts that are). To Doon and Lina, pressing issues like saving their city affect their attitudes towards everything and everyone—and since they're our main narrators, their attitudes influence how we view the events of the book.
Doon, of course, is more serious than Lina. Here's what's going on in his head after his first day working in the Pipeworks: "Running out of light bulbs, running out of power, running out of time—disaster was right around the corner. That's what Doon was thinking about when he stopped outside the Gathering Hall on his way home and saw Lina on the roof… But how could she be so lighthearted when everything was falling apart?" (3.37).
Yes, Doon, we get it: everything is Serious Business For Serious. Lina's got a dose of it too, though. Like when she loses Poppy during the blackout that happened after her colored pencil craze, she looks at the pencils and thinks, "They were not quite as beautiful as they had been. When she held them, she remembered the powerful wanting she had felt in that dusty store, and the feeling of it was mixed up with fear and shame and darkness" (5.80)
The tone here is serious because obviously it's not mocking Lina's feelings—it's presenting them realistically, and taking seriously the effect of almost losing her sister, all for some frivolous colored pencils.
Despite the fact that Doon and Lina make some mistakes along the way, we can't help but feel for them. They are, after all, only kids, ad they're doing the best they can. Like at the very end, when they've escaped Ember, Doon asks about the note they'd meant to leave with someone trustworthy:
"Oh!" Lina stared at him, stricken. "The message to Clary!" She put her hand in her pocket and pulled out the crumpled piece of paper. "I forgot all about it! All I was thinking of was getting Poppy and getting to you." (18.60)
Doh! We're kinda floored that Doon and Lina are smart enough to figure out the incomplete message from the Builders, and yet they make silly mistakes in their follow-through. But we don't end up hating them or assuming that they're idiots, and this is because the book's tone is sympathetic, giving us insights into who they are and why they act the way they do.