Here is what the LDs site says about the particular Apostacy that is being discussed:
“The gospel of Jesus Christ was lost from the earth through the apostasy that took place following the earthly ministry of Christ’s Apostles. That apostasy made necessary the restoration of the gospel. Through visions, the ministering of angels, and revelations to men on the earth, God restored the gospel. The Restoration started with the Prophet Joseph Smith (JS-H 1: 1-75; D&C 128: 20-21) and has continued to the present through the work of the Lord’s living prophets.”
"When the children of Israel failed to live up to the privileges and covenants of the Melchizedek Priesthood, the Lord took away the higher law and gave them a lesser priesthood and a lesser law (D&C 84: 23-26). These were called the Aaronic Priesthood and the law of Moses. When Jesus came to the earth, he restored the Melchizedek Priesthood to the Jews and began to build up the Church among them. However, the priesthood and the Church were lost again through apostasy. They were later restored through Joseph Smith, Jr. (D&C 27: 12-13; 128: 20; JS-H 1: 73). "
“Apostasy of the early Christian church: This people draw near me with their mouth, Isa. 29: 10, 13. Darkness shall cover the earth, Isa. 60: 2. The Lord will send a famine of hearing the words of the Lord, Amos 8: 11. There shall arise false Christs and false prophets, Matt. 24: 24. Grievous wolves shall enter in among you, Acts 20: 29. I marvel that ye are so soon removed from him, Gal. 1: 6. There will be a falling away before the Second Coming, 2 Thes. 2: 3. Some people err concerning the truth, 2 Tim. 2: 18. Some people have a form of godliness but deny the power thereof, 2 Tim. 3: 5. The time will come when they will not endure sound doctrine, 2 Tim. 4: 3-4. There will be false prophets and false teachers among the people, 2 Pet. 2: 1. Certain men crept in denying the only Lord God, Jude 1: 4. Some men said they were Apostles and were not, Rev. 2: 2. Nephi saw the formation of a great and abominable church, 1 Ne. 13: 26. The Gentiles have stumbled and built up many churches, 2 Ne. 26: 20. They have strayed from mine ordinances and have broken mine everlasting covenant, D&C 1: 15. Darkness covers the earth and gross darkness the minds of the people, D&C 112: 23. Joseph was told that the churches were all wrong; their hearts were far from God, JS-H 1: 19.”
“Moroni prophesied about apostasy in the last days, Morm. 8: 28, 31-41. Apostasy will precede the Second Coming, D&C 1: 13-16.”
No, I am not asserting their truthfulness, just presenting the claims as written at LDS-dot-org.