I remember watching in one of the versions of Ramayana on TV that Shri Rama praised Kumbhakarna as a great warrior after he was killed. Did Shri Rama respond in any manner to their deaths? If so, what was the response?
In Valmiki's Ramayana, I didn't get any reference That Rama praised Kumbhakarna after his death but when Ravana was slayed, his brother Vibhishana laments a lot, then Rama comforts him as:
वदन्तं हेतुमद्वाक्यं परिदृष्टर्थनिश्चयम् |
रामः शोकसमाविष्टमित्युवाच विभीषणम् || ६-१०९-१४
Ravana did not die in battle, without making an effort. He has fallen in combat, eventhough he was endowed with terrible prowess and exhibited extra ordinary enthusiasm of a very exalted type and remained confident throughout.
नायं विनष्टो निश्चेष्टः समरे चण्डविक्रमः |
अत्युन्नतमहोत्साहः पतितोऽयमशङ्कितः || ६-१०९-१५
There is no occasion to grieve for him having fallen into death in the battle-field and by whom the development of his country was wished for, while remaining steadfast in the duty of Kshatriya the warrior.
नैवं विनष्टाः शोच्यन्ते क्षत्रधर्मव्यवस्थिताः |
वृद्धिमाशंसमाना ये निपतन्ति रणाजिरे || ६-१०९-१६
There is no occasion to grieve for his having been brought under the sway of death by whom intelligent as he was, all the three worlds including indra were frightened.
येन सेन्द्रास्त्रयो लोकास्त्रासिता युधि धीमता |
तस्मिन् कालसमायुक्ते न कालः परिशोचितुम् || ६-१०९-१७
In the past, none has ever been exclusively victorious in a combat. A hero either has been killed by his adversaries or had killed the enemies in battle.
नैकान्तविजयो युद्धे भूतपूर्वः कदाचन |
परैर्वा हन्यते वीरः परान्वा हन्ति संयुगे || ६-१०९-१८
Such is the destiny proclaimed by the ancients, as highly esteemed for a warrior. A warrior killed in battle, does not deserve to be mourned. Such is the ascertainment of the sacred scriptures.