An elegiac tone is one of lamentation, which in "Beowulf" is typically of an allegorical nature; that is, deaths are lamented for their symbolic significance as well as for the loss of the individuals concerned. A good example of this comes at the end of the story when Beowulf slays the dragon. The creature is mourned with elegiac references to its magnificent grace, which would never again "glitter and glide," even while the loss is also an allegory for the passing of an era and of Beowulf's own death, his greatness having been spent.
This elegiac sense of fate and the inevitable passing away of things permeates "Beowulf." Despite the virtue and heroism of his confrontation with the dragon, even this event carries with it the doom of his people, since Beowulf knew he would not survive it.
Thus, the celebration of Beowulf's heroic act against the dragon is also elegiac, lamenting not only the lost hero himself but also the inevitable loss of the kingdom he left behind. The setting of "Beowulf" is a world in which kingdoms are under constant threat of invasion, which would have been offset by a feared and mighty king such as Beowulf. For this reason, Wiglaf comes to think of Beowulf's actions as lamentable, even while they may have been unavoidable.