Why did Aharon feel bad? Surely, unlike the Nesi'im, Aharon was charged with all types of Avodah (Service) in the Mishkan every day. Why did Aharon's exclusion from the one-time, voluntary inauguration of the Mishkan cause him distress, and how was the mitzvah of the Menorah to be viewed as a just compensation or portion so as to allay Aharon's feelings?
Aharon wished to be part of the Chanukas Ha-Mishkan due to its spontaneous, voluntary nature. He could serve Hashem with personal creativity rather than exclusively by routine command. Whereas his sons, Nadav and Avihu, were punished for performing Avodah based upon personal creativity, Aharon observed that God made an exception to this ban by permitting the Nesi'im to bring spontaneous, voluntary korbonos as part of a procession which they initiated. (See Rashi on 7:3.) Aharon thus felt that it was fitting that he, too, be privileged to be part of this one-time, unprecedented event.
Hashem thereupon noted that, despite the pomp and circumstance of the Chanukas Ha-Mishkan, it did not measure up to Aharon's own Avodah. Whereas the Avodah of the Nesi'im was part of a one-time celebration, Aharon's Avodah constituted an eternal routine, and the sense of commitment to perform this routine day-in and day-out reflected an even greater level of connection to God.
This is where the Menorah comes in, as part of its mitzvah - if not the entirety of the Kohen's task with the Menorah - is to clean it out and prepare it for use. The Kohen must wipe the Menorah's oil-holders clean and remove used wicks. According to some Rishonim, after cleaning out and preparing the Menorah, the Kohen then lights it, whereas other Rishonim hold that even a non-Kohen [a "zar"] may light the Menorah, for the Kohen's role is merely to clean the Menorah and set it up; lighting it is not part of his requirement. We see from this that the Kohen's mitzvah regarding the Menorah is rather "janitorial", if one can use such crass terminology.
By commanding Aharon the mitzvah of the Menorah, Hashem was affirming that the Avodah which is most precious to Him is not that of grand performance and personal creativity. Rather, Avodah which reflects submissiveness and extreme humility is what God seeks most. The Menorah embodied this type of Avodah, and it was thus the basis of Hashem's reply to Aharon's feelings of dejection.
The mitzvah of Terumas Ha-Deshen - Taking out the Ashes - is also a mitzvah of submissiveness. Nevertheless, Hashem chose the mitzvah of the Menorah to reveal His feelings about Aharon's Avodah and its import, for Chazal indicate that the Menorah's continuous light reflects the Shechinah, and God was letting Aharon and the Jewish People know that service of submissiveness and humility is the true key to merit His presence.
For a full library of divrei Torah, please see TorahHeights.com