He has faced a lot of criticism since saying he would be standing down from the assembly but continuing to lead the party from Westminster as an MP.
Party grandees including Brid Rodgers and Seamus Mallon said he should give up the leadership.
Mr Mallon, a former deputy leader, said he should go "as soon as possible".
He added that if he acted decisively it would be good for him and for the party.
In his first response to the criticism, Dr McDonnell told the BBC One programme The View that while he respected Mr Mallon's views, he did not agree with them.
"He's entitled to that point of view," he said.
"I happen to have a different point of view, and the view I'm holding is the point of view of the grassroots and the vast majority of the SDLP who want me to finish the job.
"I'm not going to run away from a task half done."
He was more dismissive of internal party critics who say if he will not resign, they may try to force a special party conference where they could mount a leadership challenge.
"We're a democratic party - people are entitled to challenge," he said.
"There's a conference scheduled for November. I have heard no word of any special conference or anything else.
"I will work within the democratic rules and regulations and standing orders that we have in the party, and I will win.
"Quite simply, what I'm doing is essential.
"The vast majority of people in the party know that it's essential and they realise that a silly personality contest or beauty contest, for want of a better description, is not going to help the party and it's not going to help the broader politics in Northern Ireland.
"Yes, I would rather people would talk to me about these issues rather than negotiate through the newspapers.
"It would be helpful but the point is this: we live in a real world, people do what they do, people are individuals in a democratic party.
"I don't have muzzles, I don't have anything else on the people and if they choose to go to newspapers or discuss things through newspapers, it's unhelpful but it's acceptable in a democratic sense."
SDLP leader Alasdair McDonnell has rounded on his internal critics, saying: "I'm not going to run away from a task half done."