The Bible says, "My friends, stop thinking like children. Think like mature people ." Children only think of themselves; grown-ups think of others. God commands, "Don't think only about your own affairs, but be interested in others, too." (Philippians 2:4 TLB)
Of course, this is a difficult mental shift because we're naturally self-absorbed; almost all advertising encourages us to think of ourselves. The only way we can make this mental switch is through a moment-by-moment dependence on God.
Fortunately, he doesn't leave us to struggle on our own: "God has given us his Spirit. That's why we don't think the same way that the people of this world think." (1 Corinthians 2:12 CEV) Begin asking the Holy Spirit to help you to think of the spiritual needs of unbelievers as you talk to them.
With practice, you can develop the habit of praying silent "breath prayers" for those you encounter. Say, "Father, help me to understand what is keeping this person from knowing you." Your goal is to figure out where they are in their spiritual journey and help bring them a step closer to knowing Christ.
You can learn how to do this by adopting the mindset of Paul who said, "I don't think about what would be good for me but about what would be good for many people so that they might be saved." (1 Corinthians 10:33 GW)