In the epic poem Beowulf, Hrothgar is told by Beowulf about the fight with Grendel in chapter fourteen (if reading the E-Text) or lines 958-980.
At the beginning of the section, Hrothgar begins by telling Beowulf that he appreciates the fact that he was able to keep his battle-boast (promise) and rid the mead hall (Heorot) of Grendel. Hrothgar states that he, too, will uphold the promise that he made--
Nothing in the world that you desire will you lack, so long as it is within my power. Often have I promised recompense for lesser deeds and given my precious hoard to a hero less famed who was less ready to fight.
Hrothgar, here, states that Beowulf will be paid handsomely for his ridding the hall of the monster.
Beowulf admits that he is sorrowful that he could not present Grendel's body to Hrothgar--he is only able to give him his arm. Beowulf states that the reason that he is not able to give to Hrothgar the body of the monster because the "Maker did not will it."
The battle itself is described by Beowulf as one which was not what Beowulf had wished. While Beowulf wished to "bind him down on his deathbed swiftly," the Grendel broke away from his grasp. Beowulf, unwilling to take the life of Grendel without being approved by God, was only able to take "his hand, arm, and shoulder in payment." Beowulf is sure that the wound will be a deadly one and that Grendel will not live long based upon the fact that he (Grendel) must "await such awful doom as the Ancient One may allot him."
Here is the exact text in which describes Beowulf's words about the fight with Grendel.
958. Beowulf spake, bairn of Ecgtheow:—
959. "This work of war most willingly
960. we have fought, this fight, and fearlessly dared
961. force of the foe. Fain, too, were I
962. hadst thou but seen himself, what time
963. the fiend in his trappings tottered to fall!
964. Swiftly, I thought, in strongest gripe
965. on his bed of death to bind him down,
966. that he in the hent of this hand of mine
967. should breathe his last: but he broke away.
968. Him I might not—the Maker willed not—
969. hinder from flight, and firm enough hold
970. the life-destroyer: too sturdy was he,
971. the ruthless, in running! For rescue, however,
972. he left behind him his hand in pledge,
973. arm and shoulder; nor aught of help
974. could the cursed one thus procure at all.
975. None the longer liveth he, loathsome fiend,
976. sunk in his sins, but sorrow holds him
977. tightly grasped in gripe of anguish,
978. in baleful bonds, where bide he must,
979. evil outlaw, such awful doom
980. as the Mighty Maker shall mete him out."