However, he insisted that Labour was tackling the problem and would be able to demonstrate progress at a scheduled meeting with Jewish leaders.
The row has been blamed for the party’s failure to secure the key target of Barnet in north London, which has a large Jewish population.
Mr McDonnell said he would meet Barnet councillors this week, adding: “Anti-Semitism certainly had its effect, there’s no doubt about it, in Barnet itself.
“I’m hoping that the measures we have put in place now, the Chakrabarti Report implemented in full, Jennie Formby the new general secretary – Jeremy Corbyn said to Jennie: ‘Your first priority is tackling this issue’.”
He said when senior Labour figures meet the Board of Deputies of British Jews and the Jewish Leadership Council again in July, they would be able to demonstrate “really positive progress”.
Labour also sought to turn its fire on the Tories, who have faced their own racism rows.
Tory Rosemary Carroll, who made a post comparing an Asian person with a dog last June, was reinstated by the Conservatives on Friday, giving the Tories narrow control of Pendle council in Lancashire.
Mr McDonnell said that reinstating her after making the “foulest racist joke” was “unacceptable”.
He said the Tory leadership should “apologise and suspend that councillor again”.
Setting out how Labour hoped to make further progress, Mr McDonnell said the party would “tour the country with detailed seminars” on economic policy and community involvement in politics.
“There are issues now about how we address those communities – this isn’t just party political any more either – that feel that their economy, which has been blighted by austerity, has left them behind,” he said.
After elections in 150 councils across England, Labour had a net gain of 82 seats and controlled the same number of authorities as before the vote.
The Tories suffered a net loss of two councils and had 96 fewer councillors.
Shadow trade secretary Barry Gardiner hailed the results but added: “Would I have liked to have done better? You bet.”
He said: “We have rightly come under the microscope for our failure to deal with anti-Semitism promptly, quickly and effectively.”