…and saying, "Men, why are you doing these things? We also are men with the same nature as you, and preach to you that you should turn from these useless things to the living God, who made the heaven, the earth, the sea, and all things that are in them, who in bygone generations allowed all nations to walk in their own ways. Nevertheless He did not leave Himself without witness, in that He did good, gave us rain from heaven and fruitful seasons, filling our hearts with food and gladness." Acts 14:15-17

What responsibility do those who know the Lord have to those who do not know Him? The short answer is to do what we can to lead them to saving faith in Christ. The slightly longer answer is to:

Pray for their salvation. Pray that God would send someone, including us, to tell them about Christ and the gospel. Ask The Lord to soften their hearts and to open their eyes and ears to receive the truth by faith—which only He can do!
Tell them about Christ. Though we need to be sure we understand the simple gospel, we are to tell what we know, even if we cannot answer every questions and/or objection people may have. We must tell what we know, no matter how simplistic our understanding may be. Remember, only God can change their hearts and save them.
Seek always to live a life that affirms, rather than undermines the gospel. Our lives save no one, but if our lives are lived in hypocrisy, we can adversely affect whether people will even listen.

God has always given revelation of Himself to all people, but the revelation is incomplete without Jesus Christ.