But Jesus made reference to the scribes and Pharisees tithing and implied that they were right in doing so. The New Covenant did not do away with the tithe but it clarified what the motives for tithing should be.
Abram tithed over 430 years before the law was given. Jacob also tithed approximately 300 years before the time of the law. Tithing was a Biblical principle that didn't begin or end with the law of Moses.
The law of Moses did include tithing as part of its commandments and attached stiff penalties for those who didn't do so. It was concerning these punishments for not tithing, that the New Testament differed from the Old Testament.
Malachi 3:8-9 says that if a man doesn't tithe, he has robbed God and is cursed with a curse. So, people gave out of debt and obligation.
Jesus redeemed us from this and all the other curses of the law, so that God will not curse us for not tithing.
The apostle Paul also made it very clear that any type of giving motivated by anything less than God's kind of love is useless. He went on to explain in 2 Corinthians 9:7, that God wants us to give, "not grudgingly, or of necessity: for God loveth a cheerful giver."
The type of giving that God loves is cheerful, freewill giving. This does not mean that tithing is contrary to the New Testament. It is the "fear of punishment" motive, that the Old Testament law attached to tithing, that has been done away with.
Giving and tithing are still very much a part of the New Testament doctrine, and if done with the New Testament attitude, are still acceptable to God. Love to be a giver.