From which Shakesperean work does the quote below come and what are the circumstances in which it is spoken?As a young as I am, I have observed...

These lines are spoken in the play Henry V.  They are spoken in Act III, Scene 2.

The words are spoken by a character identified only as "Boy."  What has happened here is that Boy, along with Pistol, Nym, and Bardolph, have retreated from the battle.  The three are sent back, but the boy stays behind.  He has decided that he no longer likes the three and is going to leave them.

In the lines you mention, he is explaining that they are really too cowardly to deserve to have him around.  He feels he is better than they are, so he leaves them.