The ITV News political editor, who spoke at the Cheltenham Literature Festival on Friday, also criticised Labour for being slow to act against anti-Semitism and said he had spoken to party leader Jeremy Corbyn.
Mr Peston said he regretted looking at eastern European migration purely as an economist.
“Looking back on it I got it wrong and I feel embarrassed about this,” he said.
“When we had all that migration from eastern Europe, people like me focused too much on the economic benefits in terms of the rate we were growing and not enough on the experience of communities.
“It is not, in my view, racist to be concerned if the composition of your community changes by something like 10 or 15 per cent points over a very small number of years.
“At the time I was at the BBC and let’s be clear, the BBC got this completely wrong – we did not listen to millions of our viewers at the time.”
Mr Peston, who described himself as a secular Jew, said Labour “has been too slow to take punitive action against people who have said some very disgusting things about Jews”.
He added: “I don’t think Jeremy Corbyn is anti-Semitic, I think he is genuinely naive, and I told him how uncomfortable I was with how slow they were to start to deal seriously with this problem.”
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