Jesus directly calls out the Scribes and Pharisees (the religious leaders of the day) who were tithing, yet neglecting the more important things that God cares about: justice, mercy, faithfulness and the love of God (Matthew 23:23; Luke 11:42). He directly affirms that they are right in tithing (these you ought to have done), but they should have also done the other important things. Jesus assumed that believers would tithe.
"...if we’re going to think about our relationship to the Old Testament (OT) tithe, I’d do it like this. Surely we’re more blessed than the OT saints. Why, then, would we assume we’d be expected to be less generous? So Christians should see the OT tithe as a kind of minimum percentage of their income to give away." –Dr. Tim Keller
Read this encouraging, helpful, and convicting quote by Dr. Randy Alcorn:
The disciples gave all that they had because “much grace was upon them all” (Acts 4:33). It was obvious from the beginning that being under grace didn’t mean that New Testament Christians would give less than their Old Testament brethren. On the contrary, it meant they would give more.
Being under grace does not mean living by lower standards than the law. Christ systematically addressed such issues as murder, adultery, and the taking of oaths and made it clear that his standards were much higher than those of the Pharisees (Matthew 5:17-48). He never lowered the bar. He always raised it. But he also empowers us by his grace to jump higher than the law demanded.
But while Jesus spoke about the tithing of the scribes and Pharisees (Matt. 23:23) during his earthly ministry, after his resurrection and the establishment of the New Testament church at Pentecost (Acts 2) the requirement to give a “tithe” or a tenth of one’s income is never explicitly imposed on Christians. Rather than stipulating a fixed amount, the NT places emphasis on generous, abundant, cheerful giving: “God loves a cheerful giver” who “sows bountifully” (2 Cor. 9:6–7), and promises that “you will be enriched in every way to be generous in every way” (2 Cor. 9:11). So, while Christians are not obligated to give a fixed amount, it is hard to imagine that God expects people of the new covenant to give any less than the 10-percent tithe in the old covenant.
The NT also encourages Christians to support the needs of the church and of those who do the work of evangelism. Paul received financial support from the church at Philippi (cf. Phil. 4:15–19), and he told churches to support their elders, “especially those who labor in preaching and teaching,” for “the laborer deserves his wages” (1 Tim. 5:17–18; cf. 1 Cor. 9:6–14; Gal. 6:6). This would require that those who are part of a church should regularly give to support the ministry of the church.