I have played a few of the STF missions and today did the first part of Infection again but after the transwarp conduit was destroyed, I saw the yellow object in space and moved toward it as the "don't forget rewards" or similar message appears. I took one of the rewards but when I checked my inventory, it was not there. I don't want to be greedy so I usually take just one reward and sometimes none, if there is not something I needed, so I was quite disappointed that the reward was not in my inventory. This has happened at other times and I think I have only gotten a reward once or twice that I took one.

What might I be doing wrong?

The drop can only go to 1 person on the team. Are you sure that you are one that received it? If not, ask your teammates if one of them got it.

Seems like the Loot Settings was not on Need or Greed, instead the leader had to have it set on Master Looter or Round Robin.