This lack of a festive meal is surprising since the most typical way that people celebrate a happy occasion is by having a festive meal, and on all other holidays there is an obligation to have a festive meal. Why is there no obligation to have a festive meal for Hanukkah? It is true that Hanukkah is not mentioned in the Torah, but Purim is also not mentioned in the Torah and there is an obligation to have a festive meal on Purim. Four different answers have been suggested based on differences between Purim and Hanukkah.
The Levush (published from 1590-1604, quoted in the Mishnah Berurah, 670:6), who seems to have been the first to ask this question, suggests that the difference between Purim and Hanukkah is that on Purim the people were in danger of being killed, but on Hanukkah the people's freedom to practice religion was threatened but not their lives. Thus, since on Purim the danger to the people was physical, then we eat which is a physical act to celebrate our salvation, but on Hanukkah the danger was spiritual so there is no need to celebrate by eating.
The Taz (670:3, 1586-1667) rejects this rationale since he points out that religious freedom is just as important as physical freedom. Instead, he slightly varies the idea of the Levush. He suggests that on Purim, a festive meal was instituted since on Purim there was a clear miracle to save the people's lives, but on Hanukkah the military victory over the Greeks was not an obvious miracle. Instead, the miracle of Hanukkah was that the oil lasted eight days, but this was a "spiritual" miracle that would not have provided as much happiness as by a miracle that saved people's lives. This distinction between the nature of the miracles of Purim and Hanukkah is difficult since one could just as easily argue that the Hasmoneans victory over the much larger Greek armies was a more obvious case of divine intervention than Esther's actions to save the Jewish people. Also, the miracle of the oil was a physical event and presumably made the people happy who saw it.
The Taz's father-in-law, the Bach (1561-1640, comments on the Tur, 670) suggests a different distinction between Purim and Hanukkah. He notes that according to Chazal, on Purim the decree that the Jews were supposed to die was in response to the people's sin of enjoying Achashverosh's party in the first chapter of Megillat Esther (Talmud Bavli, Megillah 12a). Hence, the people had to fast as part of their repentance, and the meal we have on Purim is to "fix" the initial sin of the people. However, by Hanukkah, he writes the sin of the people that caused the Greek decrees was the people's negligence by the sacrifices, and hence the "fixing" of the sin is the just the lighting of the menorah, which is related to the Bet ha-Mikdash.
A fourth suggestion is from the Maamar Mordechai (Mordechai Karmi, 1749-1825, France, commentary on the Shulchan Arukh 670:2) who notes that on Purim the people were saved by Esther's meal with Achashverosh and Haman, and hence the meal on Purim recalls the salvation of the people. However, on Hanukkah, the people's salvation was not related to eating so no meal was established.
Other possible reasons can be suggested. One reason is that it would have been difficult (expensive and time consuming) for people to have large festive meals every day for eight days. On the other hand it was not desired to institute a requirement to have a festive meal just on one day since that would have made the day more important than the other seven days. With this idea, Chazal did not institute a festival meal for practical reasons.
Another possibility is that had a meal been instituted then this might have generated discussions about the war between the Greeks and the Hasmoneans, which in turn might have led the people to try to rebel again. However, after the disastrous rebellions against the Romans in 66-70 and then by Bar Kokhba, 132-135, the idea was just to stress the candle lighting aspect of the holiday without having a meal. However, this idea would not explain why a festival meal was not made obligatory from the time of the Hasmoneans.
A final possibility for the lack of an obligatory festive meal on Hanukkah might be due to the time in the year when the holiday falls. Hanukkah can occur from the end of November to the beginning of January, which means that in certain years (as in 2016) it occurs near the time of the winter solstice, which was a time of festivals of other nations. In Greek times there were festivals for Dionysius and in Roman times the pagan holiday Saturnalia was celebrated in the end of December, for many years, on December 17-23. (The Mishnah, Avodah Zarah 1:3 refers to Saturnalia and another Roman holiday, Kalends, which apparently was celebrated a few days after Saturnalia.) On these holidays there were large feasts and hence maybe Chazal did not institute a mandatory meal on Hanukkah in order to separate Hanukkah from these other holidays. Accordingly, Chazal just instituted the reciting of Hallel (to G-d), and that the candle lighting should be in the homes (Talmud Bavli, Shabbat, 21b) to keep the celebrations of the holiday within the family and the Jewish community. This idea would accord with the notion that Hanukkah was part of the battle to remove the Greek influence from the Jews.
Rafled, Meir, 1995, Eating and happiness on Hanukkah, in Minhagei Yisrael, edited by Daniel Sperber, Jerusalem: Mossad Harav Kook, Vol. 5, pp. 85-101.