Concerning them I am asking. Not concerning the world am I asking, but concerning those whom Thou hast given Me, for they are Thine...(Concordant Literal New Testament).
Jesus was asking for a particular thing in this prayer, and it only concerned those "Thou hast given me". This is what he asked for:
Holy Father, keep them in Thy name, in which Thou hast given them to Me, that they may be one, according as We are. (v. 11).
This request did not apply to the world, because "to them the secrets of the kingdom of heaven have not been given" (Matthew 13:11). That's why Jesus was not praying for the world in this instance. I don't think we can infer that Jesus never prayed for the world, just because he didn't in this particular prayer. Nor should we assume that we are to not pray for the world.
1 I am entreating, then, first of all, that petitions, prayers, pleadings, thanksgiving be made for all mankind,
2 for kings and all those being in a superior station, that we may be leading a mild and quiet life in all devoutness and gravity,
3 for this is ideal and welcome in the sight of our Saviour, God,
4 Who wills that all mankind be saved and come into a realization of the truth. (1 Tim. 2:1-4, CLNT).