Collocations for apologetic - adj.

be, feel, look, sound

extremely, fairly, very, etc.
profusely
genuinely, sincerely
almost
Leroy sounded almost apologetic.

a little, slightly, etc.
vaguely
suitably (BrE)
I hope she was suitably apologetic afterwards.

about
He was profusely apologetic about the mistake.

for
She was apologetic for taking so long.

Apologetic is used with these nouns:
letter, look, shrug, smile