The key phrase in your question, I think, is "some level."
It is true that based on the verse you referenced, all human beings have a basic Divinely-given dignity, and we should treat them with that in mind. As Rabbi Akiva puts it (Avos 3:14, translation taken from here): "Beloved is man, for he was created in the image [of G-d]; it is a sign of even greater love that it has been made known to him that he was created in the image, as it is says, 'For in the image of G-d, He made man' (Genesis 9:6)." In other places, too, we are told that G-d grieves when even wicked people have to be destroyed (Sanhedrin 39b and 46a).
On the other hand, there's no expectation in Judaism (or in any legal system that I know of, for that matter) that everyone will be treated 100% equally all the time. So there are distinctions drawn, for legal and other purposes, between Jew and non-Jew, between man and woman, between Kohen and non-Kohen, etc. - but these are not to be allowed as an excuse to discriminate in other cases.
A mamzer's situation is actually an excellent example of this. The Torah says nothing more than that he's not allowed to marry into "the congregation of Hashem" (Deut. 23:3) - which halachah explains to mean "born Jews of kosher lineage." But he is allowed to marry another mamzer(es), or a convert or freed slave. (Shulchan Aruch (hereafter S.A.), Even HaEzer 4:1,13,22)
In most other respects, though, we treat him like any other Jew. He can get an aliyah to the Torah (S.A., Orach Chaim 282:3); sit on a beis din for anything except capital cases (Rambam, Laws of Sanhedrin 2:9 and 11:11); inherit his father's property, including the double portion if he's a firstborn (S.A., Choshen Mishpat 276:6 and 277:10); etc. If he is a Torah scholar, he even outranks other Jews who are not scholars, insofar as being earlier in line to receive charity (S.A., Yoreh De'ah 251:9).
In short, then, we try to prevent his having to shed "the tears of the oppressed" (Eccles. 4:1) - the Zohar (II:213b) in fact relates this verse to the mamzer's situation of facing marital restrictions through no fault of his own - and help him achieve as full and normal a Jewish life as possible.