Is The Atonement Incomplete?

Over the years, I had been taught by various sources that the process the chief priest went through in the tabernacle and the temple on the Day of Atonement was the same process that the Messiah would have to go through to complete God's plan of salvation for humanity. When I read the description of Jesus's crucifixion, it seemed to me, as a Christian, to be complete. After all, it was that description that had convinced me to make my conversion decision. It was only when I compared the two descriptions side by side that I discovered something was missing.Did that mean Jesus's death on the cross did not complete the process of atonement? Was the plan of salvation incomplete? How could that be? God would not allow it. I had to investigate further.As I dug into the Scripture supporting the two events, it became obvious that the crucifixion description was different from the Day of Atonement process. Why would God allow it if the missing information was essential to salvation?