P.S. Oops, I just noticed that The Random House Book of Science Fiction Stories was published in 1997 and you read your book in the early 80's. I guess this is a wrong answer then. Sorry about that!
You may be thinking of The Random House Book of Science Fiction Stories; a 5.5" by 8.5" trade paperback, it was the American edition of Space Stories, edited by Mike Ashley. If so, the closest story in that book to your description is "Status Extinct" by Eric Brown.
The "kid" is a woman space explorer:
Jessica Ball sneezed as her ship came in to land.
She blew her nose and dropped the tissue in the waste chute. She could not believe it. Modern science had developed starships to send her to the edge of the galaxy in search of intelligent life, and yet there was still no cure for the common cold.
The "miniature" aliens stand a meter tall:
The creatures were not animals—but men. They were tiny, perhaps a meter high and impossibly slim, their arms and legs as thin and gray as gun barrels. Jessica counted twenty of the tiny extraterrestrials. They moved slowly down the slope, as if wary of the strange creature lying at the bottom.
I don't believe it, she said to herself. Aliens—real, live humanoid aliens . . . She decided to call them Thinnies.
However, she is not trying to save the aliens. On the contrary, the aliens save her life after she breaks her leg, giving her first aid and hauling her back to her spaceship:
The aliens dragged the sled up the ship's ramp and left her at the top. Jessica sat up, stared at the beings who had saved her life. She raised her hand, and the Thinnies, responding to her gesture, raised their hands also before walking down the ramp and away from the ship.
The aliens were in no danger of extinction until Jessica came along:
For she had brought death to these innocent people; she had spread disease amongst them in the form of the influenza virus, a virus new to them and against which, therefore, they had no protection.
"I'm sorry," she whispered. "I'm so sorry."
She pulled the St. Christopher medallion from her pouch and dropped it into the hand of the dead alien.
The final paragraph:
She readied the ship for lift-off.
As the engines fired, she entered computer's exploration files. She typed in the information:
Planet: WINTERWORLD
Native Fauna: HUMANOID ALIENS—INTELLIGENT
Status: . . .
Jessica hesitated, tears rolling down her cheeks.
At last she typed:
Status: EXTINCT
Then the ship lifted, carrying Jessica Ball away from Winterworld forever.
The short story "Status Extinct" was identified previously as part of the answer to this question. The anthology it's in was also identified in answers to this question and this one; perhaps you will recognize the descriptions of some of the other stories.
