The abuse by clerics was committed while he was archbishop of Munich, but his aides rejected allegations of a cover-up.
Benedict did not admit to being directly to blame but asked for forgiveness for the church in his meetings with abuse survivors.
The Vatican issued a letter by him and a three-page addendum after a report released last month on abuse in the archdiocese from 1945 to 2019.
It included the alleged failure by Benedict, who was then Cardinal Joseph Ratzinger, to take action in four cases when he was archbishop of Munich between 1977 and 1982.
“I have had great responsibilities in the Catholic Church,” Benedict, 94, wrote in his first personal response to the report.
"All the greater is my pain for the abuses and the errors that occurred in those different places during the time of my mandate.
“I have come to understand that we ourselves are drawn into this grievous fault whenever we neglect it or fail to confront it with the necessary decisiveness and responsibility, as too often happened and continues to happen.
“Once again I can only express to all the victims of sexual abuse my profound shame, my deep sorrow and my heartfelt request for forgiveness.”
The letter from the former pontiff, who stepped down in 2013, was released in response to a German inquiry last month that criticised his handling of cases involving paedophile priests in the 1980s.
But organisations representing abuse victims criticised the lack of specifics in his comments.
German group Eckiger Tisch said Benedict continued a Catholic Church tradition of declaring that “there were acts and faults, but no one takes concrete responsibility".
Last month's investigation accused the former pope of knowingly failing to stop four priests accused of child sex abuse when he was archbishop.
Benedict, who is in frail health, asked a team of aides to help him respond to the lengthy findings by law firm Westpfahl Spilker Wastl, charged by the archdiocese of Munich and Freising to examine abuse over the 74 years.
The aides insisted in an accompanying statement on Tuesday that “as an archbishop, Cardinal Ratzinger was not involved in any cover-up of acts of abuse”.
In one case, a now notorious paedophile priest named Peter Hullermann was transferred to Munich from Essen in western Germany where he had been accused of abusing an 11-year-old boy.
Benedict's team has already admitted to unintentionally giving incorrect information to the report authors when they denied his attendance at a meeting about Hullermann in 1980.
But they denied any decision had been made at that meeting about reassigning the priest to pastoral duties, and on Tuesday said the abuse had not been discussed.
In his letter, Benedict expressed hurt that the “oversight” over his attendance at the 1980 meeting “was used to cast doubt on my truthfulness, and even to label me a liar".
Benedict, who lives in a former monastery within the Vatican walls, said he was grateful “for the confidence, support and prayer that Pope Francis personally expressed to me".
Before becoming pope, Benedict led the Vatican's doctrinal congregation, giving him ultimate responsibility to investigate abuse cases.