They were off doing their homework, not playing video games.
Actually, in comparison with their role in other epics (almost nonexistent!), servants ARE rather important in the Odyssey. The definition of "servant" may vary from person to person, but in ancient times most of the domestic jobs now done by paid employees were done by slaves, and housekeepers, maids, nannies, et al., were servants, whether slaves or free. So consider: the first person to whom Odysseus goes on his return to Ithaca is Eumaeus, a swinherd and slave. Later he is joined by Philoetius, a neatherd (cowherd), who is probably also a slave. If these men are not considered exactly servants, since they don't work in the palace, Eurycleia, Odysseus's old nurse, is certainly one. (The housekeeper, incidentally, is called Eurynome, although some Homeric students think that was a slip and she and Eurycleia are the same person.) Eumaeus and Philoetius fight at Odysseus's side in the battle against the suitors. Eurycleia recognizes Odysseus before he's ready to reveal his identity and becomes a valuable ally, since she bars the doors of the hall just before the battle. Then there are the disloyal servants who have been aiding the suitors--Melanthius the goatherd and the twelve maids who have been having affairs with suitors and one of whom revealed to the suitors the reason Penelope's weaving was taking so long. One might argue that what they do is less important than the aid Odysseus gets from the first three, but if that maid hadn't told on Penelope, she might still be holding the suitors off with her weaving instead of being pressured to choose a husband immediately.
Now, if you've been explicitly asked to point out how servants are still not important to the story in spite of their relatively prominent role, consider what becomes of the disloyal ones after the battle, especially the twelve maids. Their lives seem to be valued rather lightly, but of course, in aiding and abetting men who want to take over the kingdom, they HAVE committed treason.
Servants do not get much of a mention in the Odyssey - most of the stories are about the return journey of Odysseus, who comes back with crew members not servants, Any other people in the stories are slaves, so still not servants. However there are a few people who may be regarded as servants - the ex-slave swineherd Eumaeus on Ithaca, who recognises Odysseus and helps him get in the palace with the housekeeper, Eurycleia, and the goatherd Philoetius. Remember that swineherds and goatherds were very minor positions - but neither were actually servants. Just because you are employed by someone does not make you their servant (if you work on the till does not make you a servant of Tesco - although I grant you sometimes you may feel like their slave!). The only person I recognise as a servant is therefore the housekeeper, Eurycleia. However it also depends on whether you recognise dogs as servants - Argos the dog was the first on Ithaca to recognise him, and promptly dies!