(CBS News) Little more than a month after their daughter was killed in the massacre at Sandy Hook Elementary school in Newtown, Conn.,.
said the impetus for the emotional meeting, which lasted over an hour, grew out of his comments at a press conference, when he sent his prayers to the family of the shooter.
"We felt ... the olive branch had been extended for us to be able to get together and to speak and to offer condolences on both sides and just kind of get to talk as parents," Robbie explained.
Alissa Parker added that she "wanted to tell him that there was a lot of hope and opportunity to gain from this, that he held the keys" to helping them better understand the tragedy. "There was information and things to be learned from what happened and without his cooperation, it would go nowhere."
The Parkers wouldn't share exactly what was said during their meeting, but Robbie said Lanza "was very receptive to the things that we had to say. I got the impression from him that he was very grateful for the opportunity to get a chance to speak with somebody."
Still, Alissa Parker admits that she does not feel Peter Lanza should get a "pass" from taking parental responsibility for Adam Lanza's deadly shooting spree.
"I feel like he's made mistakes ... But I don't feel like he should be responsible for what happened that day," Alissa said. "That was not ultimately his decision to do that. So how can I hold him responsible for that? Were there missteps in the raising of his son? Possibly."
"The Parker Five:" Read Alissa Parker's blog
Alissa Parker addressed Adam Lanza's mother Nancy, who was killed by her son, allowing that she struggles to understand Nancy's perspective.
"Looking from the outside in, it's hard to not think that there were things that she could have saw," Alissa said. "But I'm not in her place. I don't understand their dynamics and their situation so I'm never going to understand that."
"Does she have accountability? Oh I think she has a lot of accountability. Do I think it was her fault? I'm sure that there were things that, you know, she's gonna have to be accountable for. But again, it's not my burden to carry."
Turning to her daughter's killer, Alissa spoke about whether she can find a sense of forgiveness for Adam Lanza.
What I've come to terms with is that it's not my burden to bear," she said, explaining, "I feel like I don't understand where he was at. There's so much of it that I would need to know in order to determine his accountability."
"I do hold him accountable, but I feel like God will determine that. And I feel like he's in a place where a judgment will happen, and I don't have to. I don't have to judge him. And I'm at peace with that."
For more from the Parkers on how they are helping their two young daughters cope with the sudden loss of their sister, watch the interview above.