
schmerzlich
painful
Causing mental or emotional pain; connected with grief or regret.
Der Tod seiner Großmutter war ein schmerzlicher Verlust für die ganze Familie.
The death of his grandmother was a painful loss for the whole family.
painful
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painful
Causing mental or emotional pain; connected with grief or regret.
Der Tod seiner Großmutter war ein schmerzlicher Verlust für die ganze Familie.
The death of his grandmother was a painful loss for the whole family.

to painfully miss
To miss someone or something very strongly and with emotional suffering.
Seit sie weggezogen ist, vermisse ich sie schmerzlich.
Since she moved away, I have painfully missed her.

painful
Causing physical pain or connected with it.
Er spürte ein schmerzliches Ziehen im Rücken.
He felt a painful pulling sensation in his back.
The adjective 'schmerzlich' (painful) is derived directly from the noun 'der Schmerz' (pain). The ending '-lich' turns the noun into an adjective that describes something that causes pain or feels like pain.
Die Erinnerung an diesen Tag ist für mich immer noch schmerzlich.
The memory of that day is still painful for me.
'Schmerzlich' (painfully) is very often used as an adverb to intensify a verb, especially with emotional actions such as 'vermissen' (to miss), 'bereuen' (to regret), or 'erkennen' (to realize).
Wir mussten schmerzlich erkennen, dass wir einen Fehler gemacht hatten.
We had to painfully realize that we had made a mistake.
A very common and fixed collocation is 'jemanden/etwas schmerzlich vermissen' (to painfully miss someone/something). This is a strong expression for deeply felt missing.
Seit er im Ausland studiert, vermissen ihn seine Eltern schmerzlich.
Since he has been studying abroad, his parents have painfully missed him.
In its emotional meaning, 'schmerzlich' (painful) is often combined with abstract nouns. Typical examples are 'ein schmerzlicher Verlust' (a painful loss), 'eine schmerzliche Niederlage' (a painful defeat), or 'eine schmerzliche Erfahrung' (a painful experience).
Für den Verein war der Abstieg eine schmerzliche Erfahrung.
For the club, relegation was a painful experience.
The meaning 'physical pain' is less common. You can recognize it because it refers directly to a bodily sensation or a body part.
Nach dem Sturz hatte er ein schmerzliches Gefühl im Knie.
After the fall, he had a painful feeling in his knee.
bitter
Bitter and schmerzlich can both describe a distressing realization or experience. Bitter particularly emphasizes the harsh disappointment or resentment involved. Schmerzlich focuses more on the emotional pain or regret felt.

Dass sie ihre beste Freundin verletzt hatte, war eine schmerzliche Erkenntnis.
The realization that she had hurt her best friend was painful.
Dass ihre jahrelange Arbeit umsonst war, war eine bittere Erkenntnis.
The realization that her years of work had been in vain was bitter.