Mahabharata did not say anything about his reaction after hearing the news of deaths of his disciples Bhishma, Drona and Karna.
Let us examine each case separately.
- When Parasurama fought with Bhishma on account of Amba, for 23 days, he could not defeat Bhishma. When Bhishma was about to discharge Praswapa weapon, Sage Narada stopped him, stating that he should not kill his preceptor.
In a reconciliation process, Jamadagni and his forefathers advised him as follows:
Study (of the Vedas) and practice of vows are the highest wealth of
Brahmanas! For some reason, before 'this, thou hadst been ordered by
us to take up weapons. Thou hadst then perpetrated that terrible and
unbecoming feat. Let this battle with Bhishma be thy very last, for
enough of it thou hadst already.
O thou of mighty arms, leave the combat. Blessed be thou, let this be
the very last instance of thy taking up the bow! O invincible one,
throw thy bow aside, and practice ascetic austerities
That foremost of the Pandavas, Arjuna, the mighty son of Indra, hath
been ordained by the Self-create to be the slayer of Bhishma!'
So Parasurama knew beforehand that Arjuna will be the cause of elimination of Bhishma. So he should not have any qualms at the death of Bhishma.
- In order to demoralise Drona, Bhimasena killed an elephant with the name Aswatthaman, and proclaimed before Drona that he had killed Aswatthaman. Drona thought it was Aswatthaman, his son, but still he continued his battle.
Beholding Drona stationed on the field for the extermination of the Kshatriya race, the Rishis Viswamitra, and Jamadagni, and Bharadwaja, and Gautama, and Vasishtha, and Kasyapa, and Atri, and the Srikatas, the Prisnis, Garga, the Valkhilyas, the Marichis, the descendants of Bhrigu and Angiras, and diverse other sages of subtle forms quickly came thither, with the Bearer of sacrificial libations at their head, and, desirous of taking Drona unto the region of Brahman, addressed Drona, that ornament of battle, and said,
'Thou art fighting unrighteously. The hour of thy death is come.
Laying aside thy weapons in battle, O Drona, behold us stationed here.
After this, it behoveth thee not to perpetrate such exceedingly cruel
Thou art versed in the Vedas and their branches. Thou art devoted to
the duties enjoined by truth, especially, thou art a Brahmana.
Such acts do not become thee. Lay aside thy weapons. Drive away
the film of error that shrouds thee. Adhere now to the eternal path.
The period for which thou art to dwell in the world of men is now
full. Thou hast, with the Brahma weapon, burnt men on earth that are
unacquainted with weapons.
This act that thou hast perpetrated, O regenerate one, is not
righteous. Lay aside thy weapons in battle without delay, O Drona, do
not wait longer on earth. Do not, O regenerate one, perpetrate such a
Being a brAhmana, Drona should not have acted like a kshatriya. He took weapons and killed many warriors like a kshatriya. That was why the rishis warned him to desist from doing further, including the descendants of Bhrigu.
We have to remember that Parasurama also a descendant of Bhrigu.
As Drona did a mistake, unbecoming of a brAhmana and took the path of a kshatriya, Parasurama, who himself decided not to take bow after the war with Bhishma, should not have regrets at the death of Drona.
- As far as Karna is concerned, we have to remember that Karna learnt usage of Divine weapons from Parasurama, by telling untruth that he was a brAhmana. So Parasurama should not have regretted for the death of Karna.