Everyone tried to fight Kakashi on their own, making it easy for Kakashi to pick them off one by one. After instructing them to not feed Naruto, he's happy to see the team going against his orders ...
That said, Kakashi still had the opportunity to gain the Rinnegan at one point later down the line, although the idea was quickly squashed by the author. After losing his Mangekyo Sharingan ...
Kakashi's ability to copy jutsu with his Sharingan makes it possible for him to have copied the Rasengan, but it's unlikely ...