Put down my prefix:
diss: to diss is to insult or “put down”
Put on my suffix:
ointment: ointment is something that is "put on" (thanks @Chowzen in the comments)
You can’t see my infix for the trees:
sap: “Can’t see the wood for the trees” is an expression. “sap” is found inside trees.
If I had a cape, it would look like this:
The image is of the goddess Columbia (per the website linked). Cape Disappointment is the cape on the north of the Columbia River.
Disappointment Island is part of the Auckland archipelago.
Not as good as I hoped: a disappointment.