Unless the 4/5th who died were completely separate set of families from those who left, each family that left would probably have lost a significant number of close family members. Would it not then be reasonable that the ones who survived and left would be in a state of mourning (and perhaps shock, and depression)? How could they then appreciate the Exodus, sing praises to G-d at the sea, or really focus on anything else - from a simply psychological perspective?
Beautiful question! The Belzer Rebbe asks it as well and says,
"As lofty and climactic a moment as Shiras HaYam (Song of the Sea) may have appeared to the naked eye, for those who were actually living through it, it was bittersweet. While they were certainly grateful and appreciative for their miraculous salvation from the hands of their sadistic Egyptian oppressors, the majority of the Jewish people were not there to experience it, as Rashi writes (13:18) that four-fifths of the nation died during the plague of darkness and did not merit the redemption. If 80% of the Jewish people died in such a short period of time, it is safe to assume that virtually everybody who did merit being saved had relatives who were not as fortunate. As such, as great as their personal feelings of joy and relief may have been, they were tempered by the recognition that they were unable to share them with their loved ones who had recently passed away.
The Rebbe posited that when Moshe came to the Jewish people and suggested that they all sing a song of praise to Hashem, they responded in disbelief, "How can you expect us to be capable of singing? Four-fifths of Klal Yisroel is missing!" When Moshe heard that, he told them that the Torah's discussion of the very song he wanted them to sing hints to the future resurrection, at which time they will be reunited with all of their deceased friends and relatives. This awareness consoled the people and cheered them up so that they were able to sing with joyous hearts, a thought which also comforted the grieving Belzer Chassidim and enabled them to open up and sing Shabbos zemiros with their Rebbe."