In the May 17 episode of the long-running BBC One soap, Peggy took an overdose after breaking the news to son Grant Mitchell (Ross Kemp) that her cancer had returned.
Alistair Thompson, a Christian from the group Care Not Killing, had told Premier the BBC was "promoting assisted suicide yet again".
He said: "It's so sad that the BBC are taking the easy option in promoting assisted suicide yet again, which they have done on a number of occasions, rather than looking at the much bigger issue which is how do we look after people that are terminally ill."
During an interview with The Huffington Post UK, Dame Barbara said: "I believe that we must respect both sides of the argument, but I believe the producers did everything they could to take care over such a sensitive subject matter.
She added: "Both the Samaritans and health specialist that EastEnders worked with on the storyline have praised them for the way it was handled."
The BBC Press Office told Premier: "EastEnders has a rich history of tackling difficult social issues and Peggy's story is one of these.
"We have worked closely with leading medical experts and various charities, including the Samaritans, to ensure that this storyline is portrayed as sensitively and responsibly as possible.
"At no point do we glamourise or romanticise the issue of suicide, in fact we have taken great care to show the audience not only Peggy's perspective but the many different views of those around her."