Mr Adams, who will be 70 next year, said on Sunday that those killed during the Troubles cannot be brought back, but that it is possible to ensure history is not repeated.
He said he and the late Martin McGuinness helped to bring about political change and that there is no reason for anyone else to die because of political conflict on the island of Ireland.
Mr Adams was speaking just hours after he told a Sinn Fein Ard Fheis that he will step down as party president next year and will not contest the next general election in Ireland.
As he announced his departure from frontline politics on Saturday night he received a standing ovation from over 2,500 delegates who gathered in Dublin’s RDS to hear his plans for the future.
Linfield v Portadown Sunday clash: Breakers of the Sabbath will answer to God
College lecturer dies while on holiday
Tom Topping: Heartbroken daughter says ‘world is totally shattered’ after father’s shock death - funeral details released
Michelle O’Neill has kicked sand in the face of victims of terrorism
‘Holistic and inclusive’: Northern Ireland Office Wilton Park report so full of ‘lazy jargon’ it makes you ‘lose the will to live’
It was noted by some critics that he did not mention any victims of IRA violence during his speech.
Commenting on the criticism, he said: “There have been many victims. I have a particular affinity with those who were victims of the IRA because obviously throughout my political life I have defended the IRA. But I understand how people feel.”
Speaking on RTE’s The Week In Politics, he added: “The war is over. One of the great achievements - and that will not bring back the dead - but one of the great achievements in Irish history - John Hume was there, others were there, but I and Martin McGuinness were there - was to bring about a peace process. We have to go forward.”
Mr Adams said he lost family members during the Troubles, that he himself had been shot and that his neighbours in Ballymurphy in West Belfast are still waiting for an inquest more than four decades after the Ballymurphy massacre.
“We can’t bring those folks back but what we can do is to ensure it never ever happens again,” Mr Adams said.
He added: “One of our second achievements has been to bring about democratic, peaceful means, bringing about political change that didn’t exist before so there is never ever going to be any reason, and it is my firm hope that hopefully no one else will die because of political conflict on this island.”
Mr Adams said the next Sinn Fein president will be appointed through a democratic process at the Ard Fheis next year.
The TD for Co Louth, who has been party president since 1983, told the annual conference on Saturday night: “Leadership means knowing when it is time for change and that time is now.”
Mr Adams said the move was part of the ongoing process of leadership transition within the party.
The plan, formulated along with Martin McGuinness before his death earlier this year, has already seen Michelle O’Neill, 40, take the role of Sinn Fein’s leader at Stormont.
The Ard Fheis also saw the party faithful debate its position on abortion.
Delegates voted to partially liberalise the party’s stance, setting its position ahead of next year’s referendum in the Irish Republic on the clause of the state’s constitution that frames its strict laws on terminations.
The conference was the first held since Mr McGuinness died in March. His widow Bernie attended as tributes were paid to the former IRA commander turned Stormont deputy first minister.