Yes, our greatest desire in our giving should be to serve God, not to gain some advantage for ourselves. We should be like the Christians in Macedonia whom Paul commended, because "they gave as much as they were able, and even beyond their ability" (2 Corinthians 8:3)–all without the benefit of any tax deduction!
I'm grateful our government realizes that churches and other organizations make an important contribution to our society, and for that reason it grants them exemption from taxes. If they weren't helping the poor and doing educational work and serving others in a host of other ways, the government would have to take up the slack–and wouldn't be able to do it as efficiently or compassionately. Many countries don't have the same outlook.
At the same time, everything we have–including our money–has been given to us by God, and we are only stewards or trustees of it. If we are Christians, our goal should be to serve Christ in every way we can–including with our money.
Make sure of your commitment to Jesus Christ, and then ask Him to help you use your money the way He wants you to. Through your giving, you can touch the lives of people you will never meet this side of eternity. The Bible says we should give joyfully, "for God loves a cheerful giver" (2 Corinthians 9:7).