Why does Padme react this way after the Tusken incident?

She's comforting him because she cares about him. He's become very dear to her in their travels. But the main reason is that she can see he's really cut up about it. She can see he's affected by how he let his anger go, and he's horrified at himself for killing them all. Yes, he hates them for killing his mother, but at the same time, he hates himself for doing what he did. He knows it's not the Jedi way, and he knows that what he did was wrong.

Padme, on the other hand, understands where the rage comes from. She understands that it would only be human to feel as he did, and to want revenge. Especially after having met his mother herself, and knowing how much Ani loved his mother. So she understands why he did what he did.

She also understands that he is beating himself up about it, because he's trying so hard to be a proper Jedi. He's visibly hurting, not only because of his mother's death, but also because of how he took revenge on all the Tuskans. She doesn't need to berate him, cos he's already doing it to himself. What she sees now is that he's conflicted inside, and she's trying to reconcile him to it.

I'd bet, if she had been there, she's have stopped him. She'd have tried to tell him to walk away and to remember that he's a Jedi. But the thing is, it already happened, and there's nothing she or anyone else can do about it. She knows he's a good boy, and that he didn't slaughter them all for fun. He was angry and in pain, so he did it without fully thinking. She can see by his guilt that he knows his own mistake. All she's trying to do now is help him come to terms with what wrong he did, and move on.

After all, she loves him.

She's overwhelmed by the situation

Padmé sat back a bit, too stunned to respond. She knew that Anakin needed her to say something or do something, but she was paralyzed.

—Attack of the Clones (novelization)

As we also see here:

Padmé pulled him in and hugged him close, never wanting to let go. She still didn’t know what to say.

“Why do I hate them?” Anakin asked her.

“Do you hate them, or do you hate what they did to your mother?”

“I hate them!” he insisted.

“And they earned your anger, Anakin.”

—Attack of the Clones (novelization)

At the moment, she's a bit too shocked to spend too much time thinking of the morality of the situation.

She cares for Anakin

We cannot underestimate how much caring for a person can lead someone to overlook their misdeeds. Padme's first reaction is to back up and comfort Anakin, not condemn his actions. That doesn't mean that, coming from an objective standpoint, she might not disagree with what he did.

She views it as justice

“Do you hate them, or do you hate what they did to your mother?”

“I hate them!” he insisted.

“And they earned your anger, Anakin.”

—Attack of the Clones (novelization)

Don't forget, while Anakin's revenge was vicious and disproportionate, the Tuskens had tortured and killed his mother. Padme seems to view his anger and actions as justified when seen in that light.

That said, this attitude might not have been shared by the courts of Coruscant, which is probably why Anakin kept it quiet. There is no doubt that Padme's reaction here is colored by her friendship with and feelings toward Anakin. There is also no doubt that this was a contributing factor in Anakin's fall to the Dark Side later on.

In addition to the other answers:

The sand people are viewed as sub human.

The question even states this

ANAKIN: I-- I killed them. I killed them all. They're dead. Every single one of them. And not just the men... but the women... and the children too. They're like animals, and I slaughtered them like animals! I hate them!

The (old EU) novel Kenobi goes into depth on the relation between the sand people and the settlers. While the settlers fear the sand people they think that even trying to communicate with them is pointless as they are no more than animals. (it must be said the sand people also think the settlers are sub-sand person)

If a herd of buffalo stampeded over your mother, would slaughtering them seem so overblown.

It's interesting that after three years, Anakin felt guilt over his slaughter of the Tuskens, despite the fact that they had killed his mother. Yet, Padme had not given them a second thought. Then I remembered how Cliegg Lars described them - "Those Tuskens walk like men, but they're vicious, mindless monsters."

Padme regarded Anakin's actions against the Tuskens as "justice". She regarded the Tuskens' actions against Shmi, and Anakin's actions against the Jedi as "monstrous". She saw nothing wrong with Anakin enacting revenge against the Tuskens. She never considered the idea that revenge is not justice. Ironically, Anakin did.

This is not about bad writing on George Lucas' part. This is about Lucas revealing that Padme was never the ideal female character that many fans wanted her to be.