There is no doubt in my mind that Christ observed the feast days of the Old Testament (Mark 14:12; Luke 2:42; 22:1; John 2:23; 7:8, 14), and that he expected His disciples to do so, too (John 7:8). And, of course, the feast days of the OT had corresponding days of fasting (Lev. 23:28-32). Certainly, no one can dispute the presence of sacrifice-- personal and corporate-- in the OT, and while Christ is the fulfillment of the ceremonial law, we nevertheless glean a good bit of our worship practices from these portions (such as fellowship offerings, thank offerings, etc.). Christ commanded this, too: just as the Israelites were commanded to deny themselves (Lev. 23:32), so too Christ demanded a spirit of sacrifice from His disciples (Matt. 16:23; cf. Mark 8:34; Muke 9:23).
There is also the model of Christ Himself fasting for 40 days (Luke 4:1-13); why did He fast? To prepare for His public ministry, in which He would bring "the good news of the kingdom of God" (Luke 4:43). This was unique because it was Christ, but it wasn't original: Moses, also, fasted for 40 days (Ex. 34:28) for what? In preparation for the words of the covenant, the Ten Commandments-- if you will, the good news of the kingdom of God. The pattern of a time period of "40" is imposed upon Israel in their desert wandering, as well; to what end? To prepare them for entrance into Canaan-- in other words, for preparation for the fulfillment of covenantal promise of good news of the kingdom of God.
Scheduled/patterned days and times of fasting were never rejected by Jesus; rather, when He taught about the patterned fasting of twice a week by the Pharisees (Matt. 6:16-18), He was pointing out their hypocrisy as the problem, not their patterned fasting. He assertion, "when you fast..." (Matt. 6:16, 17), implies that He expected them to continue in a patterned fasting. If you want to argue that He opposed regular fasting in this way, you also set the stage for His opposition to giving to the poor (Matt. 6:2) and prayer (Matt. 6:5)! In fact, in His only other teaching on fasting, Jesus stated outright that, after He had ascended, we (his disciples) WOULD fast until His return (Mark 2:18-22).
It is clear that, by the time of the Didache [which is the collected teachings of the Apostles], the expected routine fasting was a normal practice of Christians, refraining from the hypocritical patterns of the Pharisees. Didache 8:1 says, "But do not let your fasts coincide with those of the hypocrites. They fast on Monday and Thursday, so you must fast on Wednesday and Friday." And this sort of patterned, scheduled fasting continued well into the Reformation and beyond-- with only our more modern era rejecting regular fasting as a way of Christian experience, probably because we are much more gnostic than we dare to admit.
Furthermore, the earliest Christians (that we have any records of, apart from Scripture) apparently observed Lent because they believed that the apostles themselves had commanded it. It is mentioned in The Constitutions of the Holy Apostles (similar to the Didache) Book V, section III-- “On Feast Days and Fast Days”:
Brethren, observe the festival days; and first of all the birthday which you are to celebrate on the twenty-fifth of the ninth month; after which let the Epiphany be to you the most honoured, in which the Lord made to you a display of His own Godhead, and let it take place on the sixth of the tenth month; after which the fast of Lent is to be observed by you as containing a memorial of our Lord’s mode of life and legislation. But let this solemnity be observed before the fast of the passover, beginning from the second day of the week, and ending at the day of the preparation. After which solemnities, breaking off your fast, begin the holy week of the passover, fasting in the same all of you with fear and trembling, praying in them for those that are about to perish.
Did the New Testament church observe Lent as we see it today? No, because they were essentially continuing to follow the calendar of the Jewish tradition. Neither did they observe Christmas, Easter, or any other of our calendar observances as we have them today. Did you remark anything about it being Christmas on December 25 at your church? Will there be mention of Easter on April 12? My guess is, of course! If not, then I would suggest that, at least in MOST churches (that don't follow a liturgical calendar), they still have a calendrical pattern; it just happens to be dictated by Hallmark instead of church history!