Paul does not tell the Thessalonians that they should not grieve at all concerning their loved ones who have died, but he writes, "that you may not grieve as others do who have no hope" (1 Thess.4:13) —they should not grieve in the same way, with the same bitter despair, that unbelievers have. But certainly they should grieve.
He assures them that Christ "died for us so that whether we wake or sleep we might live with him" (1 Thess. 5:10), and thereby encourages them that those who have died have gone to be with the Lord. That is why Scripture can say, "Blessed are the dead who die in the Lord henceforth . . . that they may rest from their labors" (Revelation 14:13). In fact, Scripture even tells us, "Precious in the sight of the LORD is the death of his saints" (Psalm 116:15).
Therefore, though we have genuine sorrow when Christian friends and relatives die, we also can say with Scripture, "O death, where is your victory? O death, where is your sting? . . . Thanks be to God, who gives us the victory through our Lord Jesus Christ" (1 Corinthians 15:55-57). Though we mourn, our mourning should be mixed with worship of God and thanksgiving for the life of the loved one who has died.