Earlier this week police were called in to control a protest in Khayelitsha.
De Lille said there was no need for the youth league to foment illegal protests and genuine grievances should be addressed through the proper channels.
"All of these wards have been won by ANC councillors. The first thing a community must do, when you've elected a councillor and you have a grievance, is go to your councillor. The councillor takes up your grievance," she said.
De Lille said that the community's grievances could not justify the destruction of property, attacks on passersby and the deaths that had resulted from the protests. "It cannot be acceptable in a normal democracy," she said.
While De Lille said she accepted that inequality was a serious problem in Cape Town, she said it was unfair to single out the city from other South African cities.
De Lille has condemned the ongoing service delivery protests in the Western Cape as political and said the ANC "cannot accept" that the it is not in power in the Western Cape.
"These are not service delivery protests. They are illegal ANC-organised protests with the express purpose of destroying property," said De Lille.
On Tuesday De Lille and DA leader Helen Zille wrote to President Jacob Zuma asking him to condemn a "sustained and co-ordinated campaign" by the youth league over the last two weeks to incite violent protests in Cape Town.
Poor opposition
The party has submitted a dossier of evidence concerning the protests to law enforcement officials for investigation.
Over the past week, four people, including a toddler, have died as a result of the protests in the Western Cape. The demonstrations have also reportedly caused R5-million worth of damage and cost over R600 000 in overtime for law enforcement officers.
The DA said the youth league had "all but admitted" responsibility for the violence but that the only words that had come from the ANC were justification of the youth league's campaign.
Earlier this week Western Cape ANC chairperson Marius Fransman dismissed allegations that the youth league was behind the protests and said the protests were caused by a lack of service delivery.
But De Lille told the Mail & Guardian that the underlying issue was that the ANC cannot accept that it is not in government in the Western Cape.
"They cannot get used to being the opposition in the only province where they are not in charge," she said, adding that the ANC must "learn how to be good opposition".
"If you are good opposition, you hold the government of the day to account, you ask questions and bring up debates," she said.
Youth league denies involvement
Meanwhile, Khaya Yozi, ANC Youth League leader in the Dullah Omar region, said the youth league has been unfairly implicated in the protest action.
"We've got absolutely nothing to do with it," he said. "[De Lille and Zille] are tarnishing the name and image of the youth league. This is a strategy to defocus us from raising critical issues. They want to drag us to court."
Yozi said the youth league had called on individuals who are frustrated to refrain from using violence and to operate within the legal framework.
He added that when the youth league said it would make the province "ungovernable", it meant that members would march to the economic hub of the province to protest legally.
Yozi dismissed De Lille's argument that grievances should be escalated through local government channels, saying ANC councillors and representatives were constantly outvoted by their DA counterparts in portfolio committees and the City's mayoral committee.
"It's useless when those who are in power ignore [you]," he said. "The DA is only considering servicing those people who voted it into power."
"Madam Zille does not give a damn about our conditions here."
Delivery hotspot
The Western Cape has been a hotspot for service delivery protests this year. Almost a quarter of all protests in the country this year have taken place in the province.
Karen Heese of Municipal IQ, which has been tracking service delivery protests around the country, said protests in Cape Town have the same root causes as in any other metro area.
"High rates of urbanisation, which puts pressure on housing delivery and failing this, rapid growth of informal settlements where living conditions are appalling and especially so in winter," she said.
"Of course the Western Cape has a whole additional layer of racialised politics and contested inter-party tension and this I think has accelerated protests and violence in recent months.
Heese said that while the Western Cape has one of the lowest poverty rates in the country, it also has one of the highest levels of inequality, which creates a heightened sense of relative deprivation.
"In terms of free basic service delivery, Cape Town has always done very well," said Heese but "the spatial layout of Cape Town makes any investment in economic infrastructure, [that is] not on the Cape Flats, a conspicuous investment away from the poor".
This was exacerbated by the DA's poor credibility when communicating its long-term development plans to the poor.
However, Heese said, the ANC should be more circumspect in its criticism of Cape Town as the same conditions exist in other cities.
In a report on the state of the world's cities, UN Habitat found that the three most unequal cities in 2010 were Buffalo City in East London, Johannesburg and Ekurhuleni.