Q:

Which part is the tail in 人参{にんじん}の尻尾{しっぽ}

What is meant by a "carrot tail"? 

人参{にんじん}の尻尾{しっぽ}

Is it the green part or the orange part? 
A google image search does not really help, since "carrot" comes up in every one, but no picture I have found has arrows with labels for the parts of a carrot :D
https://recipe.rakuten.co.jp/word/%E4%BA%BA%E5%8F%82%E3%81%AE%E5%B0%BB%E5%B0%BE/

A:

It is the tip of the orange part, not leaves of carrot. 

A:

As @Yuuichi Tam says, this is the orange thin part of the root.  You could also have deduced this by elimination: the green part would undoubtedly be 人参の葉っぱ (also in recipes).