I blamed him for (losing or wasting) my pen.
Location: Santa Cruz, California, US
Of the two, only "losing" works. We generally do not speak of wasting a pen. However, we could also say:
I blamed him for ruining my pen.
Location: Sacramento, California
"Blame" is a verb that takes a special alternation whereby the same idea can be formulated in two different but closely related ways. Letting "it" replace the gerund "losing my pen," we may phrase the sentence in either of the following two ways:
(1) I blamed him FOR it.
(2) I blamed it ON him.