roundly
loudly
aloud
quietly, softly, under your breath
He cursed under his breath as the hammer slipped.

inwardly, mentally, silently
angrily

for
I cursed her roundly for being late.

curse and swear (BrE)
curse and shout, yell, scream, etc.
She was cursing and screaming at me just because I was late.

curse the day
He was now cursing the day he ever got involved.

curse your luck
She cursed her luck that she had had to wait for so long.

Curse is used with these nouns as the object:
fate, stupidity