"On a personal level, I find this very difficult and I'm not going to cry..." she said, with her voice cracking with emotion.
"But, you know, to read the submissions and to read how much faith they put in me personally as their member of Parliament and to read that people feel that in electing me as their mayor that I would stand up for the east and to read how let down people feel in me... All I really want to do is say I am really sorry.
"There is no intention around this table to let anyone down and the wonderful thing that has come of this terrible process, which we will never repeat, I promise that, and the wonderful thing that has come from it, is that there isn't a member of this council that doesn't understand how important it is to prioritise work in the east."
Almost 2000 submissions were made during the LTP consultation process.
Many submitters from the eastern suburbs spoke of their frustrations at being "forgotten".
"I wish the mayor would remember the east like we all expected," one submitter said.
"We have been forgotten and yet pay high rates."
However, most of the criticism was aimed at the council as a whole, and not Ms Dalziel personally.
Burwood/Pegasus community board chairwoman Andrea Cummings nonetheless welcomed the mayor's apology.
"It was really appreciated by those who know how hard it is out in the east," she said.
"It's good to not feel forgotten, which is what the community has felt for a long time."
The LTP process has united the community and has given them an opportunity to be heard and feel empowered, Ms Cummings said.