Who are Jesus' sheep?

Here is a question.  When the Scripture below says "feed My lambs", "tend My sheep", and "feed My sheep"; who exactly are Jesus' sheep?  Is it a general every single person in the world because "God loves everybody" type of thing?  Or is it referring to a specific group of people? 

John 21:15-19(NKJV)

So when they had eaten breakfast, Jesus said to Simon Peter, “Simon, son of Jonah, do you love Me more than these?” He said to Him, “Yes, Lord; You know that I love You.” He said to him, “Feed My lambs.”

He said to him again a second time, “Simon, son of Jonah, do you love Me?” He said to Him, “Yes, Lord; You know that I love You.” He said to him, “Tend My sheep.”

He said to him the third time, “Simon, son of Jonah, do you love Me?” Peter was grieved because He said to him the third time, “Do you love Me?” And he said to Him, “Lord, You know all things; You know that I love You.” Jesus said to him, “Feed My sheep. 

Most assuredly, I say to you, when you were younger, you girded yourself and walked where you wished; but when you are old, you will stretch out your hands, and another will gird you and carry you where you do not wish.” 

This He spoke, signifying by what death he would glorify God. And when He had spoken this, He said to him, “Follow Me.”

As I've mentioned before I think sometimes Scripture is applied with too broad of a brush.  I'll use this Scripture to make my point.  There are many who seem to think that because God loves everyone that that means that everyone is entitled to the benefits of believing in Jesus, whether they actually believe in Him or not.  I don't believe that is true. 

So here is some Scripture that I believe is clearly singling out a specific group of people that Jesus is telling Peter to look after.  In the Scripture above I think the fact that My is capitalized signifies that Jesus is referring specifically those who follow Jesus, to the exclusion of the rest.  

Why do I think that?  Because Jesus has clearly said in other Scripture who exactly His sheep are.  Take a look.

John 10:27(NKJV)

My sheep hear My voice, and I know them, and they follow Me. 

"…and they follow me.".  Therefore logic dictates that those who don't follow Jesus and have rejected Him, are not His sheep.  They are not entitled to the benefits of being one of Jesus' sheep.  Make sense?