Paul made note of this verse in defending his ministry to the Gentiles when the Jews of Antioch rejected the gospel:
Acts 13:This gives us insight as to the application of this verse. When we present the gospel to those around us we are fulfilling this prophecy. The Lord Jesus is bringing salvation to the ends of the earth through us - the Christian community.
45 When the Jews saw the crowds, they were filled with jealousy and talked abusively against what Paul was saying.
46 Then Paul and Barnabas answered them boldly: "We had to speak the word of God to you first. Since you reject it and do not consider yourselves worthy of eternal life, we now turn to the Gentiles.
47 For this is what the Lord has commanded us: "‘I have made you a light for the Gentiles, that you may bring salvation to the ends of the earth.’"
48 When the Gentiles heard this, they were glad and honored the word of the Lord; and all who were appointed for eternal life believed.
Another aspect of this verse in Isaiah is the idea that God is not satisfied with giving out small things to His Christ. By analogy I would think this would apply also to followers of Christ. God wants to make a large effect upon the world through us. While we may experience personal failure in ministry as Jesus did, yet there is the long term impact to consider. For Abraham had but one son of promise before he died and yet was promised to have descendents as sands of the sea shore or stars in the sky. Later we see Isaiah applying this to God's people saying, "The least of you will become a thousand, the smallest a mighty nation. I am the LORD; in its time I will do this swiftly." Isaiah 60:22