In front of this problem you have three solutions, build a uvmapping making seams in parts that separate the object or directly never or almost never are visible in-game, for example, in a human model it could be in parts where objects or hair will go.
Now another way is to manipulate the texture using an image editor, like GIMP.
The third is to keep using the filter, I recommend this filter, it is beautiful in its own way, and you have to look at a lot of details in a very low resolution texture for this to be clearly noticeable.
With what I will give below two problems will be solved, the noise in images (like a bake in Blender), and the pixelization problem.
I will load the model using the bilinear filter:
I will deactivate the bilinear filter:
I will open the image texture with Gimp and apply Noise Reduction(Filters->Enhance->Noise reduction->OK button)
Result:
So far so good, but zooming out still shows traces of pixelization:
I will edit the image again with Gimp, this time I will use Gaussian Blur(Filters->Blur->Gaussian Blur->OK button)
That's it's, the head is part of a robot that I will prepare as a free asset with cc0 license soon.
