Along the same line, John Piper in his sermon "How to Give Away a GIFT" says, "I have never been very good at turning a conversation with an unbeliever into a serious spiritual discussion of his condition before God." I can identify with that as well.
Piper has a few practical insights, emphasizing our need for prayer:
Probably the most helpful thing anybody ever told me about becoming a good witness is this: be honest with God about how you feel and then ask Him earnestly to take you where you are and give you some opportunities for witness that you can handle at this stage and grow by. Very few changes happen overnight in the Christian life. Most of us grow slowly and by fits and starts. But even that will only happen if we are earnestly praying that it will.
He goes on to say:
I suppose I could content myself under the sovereignty of the Holy Spirit and say that He has called me to be a pastor-teacher not an evangelist. But I am a dyed-in-the-wool hedonist. I want to be as happy as I can possibly be in this life and in the life to come. And now I have seen in the Word and tasted in experience that there is a joy to be had out there in telling others about why I have hope in Christ, and I want that joy. So unless the Lord makes it very clear to me that I must, I am not going to accept my lack of giftedness in evangelism. I have been praying and will go right on praying and ask you to pray with me that God will give me the gift to win people to Christ, one-to-one and through my preaching.
This is good counsel for the many of us who "stink" at evangelism. Pray that the Lord of the harvest will empower us to make Jesus known.