David Baddiel has told ITV News that David Cameron has not understood the wider context of the word "Yid".
Mr Cameron told the Jewish Chronicle that Spurs fans who use the term should not be prosecuted. But many find the term anti-Semitic and offensive.
The comedian told UK Editor Lucy Manning that the Prime Minister would not let another racist term "pass his lips":
Watch Lucy Manning's report on ITV News at 6.30pm
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The suspect, 35-year-old Willie Corey Godbolt, has been arrested and was being treated for a gunshot wound in hospital.
Mohanna Abdhou, known as Montana, was out with friends when two attackers cycled up to them and opened fire in Brent, north-west London.
The US president tweeted that Mrs May gave him "full details" of the incident during talks while he attended summits in Europe.