"We have not explained what democracy is. Democracy is complex. At times, among the protesters, you find comrades who have not understood democracy," he said.
Speaking to almost 2 000 delegates at the South African Communist Party's 13th National Congress, Zuma questioned whether protesters had a democratic right to destroy property.
In an address that lasted almost 90 minutes, he praised the SACP, saying it had played a critical role in the ANC, but it had to determine how influential it would be in the future.
"The party will not be influential if it is not armed with the revolutionary theory."
Zuma echoed earlier comments by Congress of South African Trade Unions (Cosatu) general secretary Zwelinzima Vavi, who said that a "radical approach is needed on the economic front".
Zuma said the country's economic policies for improving the lot of ordinary South Africans "doesn't seem to be working".
Continuing unemployment and casualisation of labour were a grave threat to the tripartite alliance.
"We are struggling to find solutions to defeat poverty and inequality," Zuma said.
Earlier, Vavi said the ANC risked losing working class support unless it tackled poverty immediately.
"The liberation movement has the risk of falling out of favour with the working class," he told the conference.
In his address, Vavi said members of the tripartite alliance agreed on what needed to be done but lacked political will, "which leaves much to be desired".
He said on average the position of black South Africans had deteriorated since the advent of democracy in 1994.
"We have not benefited for the past 18 years. There is no debate [on this fact]. In economic terms it is capital that has ripped the fruit of our hard-earned freedom."
He said that for economic transformation there needed to be unity in the tripartite alliance.
"No economic transformation can be led by a divided factionalised organisation."
Vavi said that the working class was angry and frustrated because the "apartheid fault lines remained, in economic terms".
"There has been a reverse redistribution from the poor to the rich."
He said blacks on average tended to earn eight times less than whites – the same income inequality that existed in 1962 at the height of apartheid. – Sapa