The PM was responding to Tory party chairman Oliver Dowden saying it could not be "business as usual" as he quit.
Mr Johnson told BBC Radio 4's Today programme, he "humbly and sincerely" accepts criticism.
But he said he also had to distinguish between "criticism that really matters and criticism that doesn't".

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The by-election defeats in Wakefield and Tiverton and Honiton on Friday came after the prime minister faced months of criticism over parties in Downing Street during lockdown, alongside soaring inflation and a narrower-than-expected win in a confidence vote from his own MPs.
Speaking from the Commonwealth heads of government meeting in Rwanda, Mr Johnson repeatedly said that policy was more important than allegations about his conduct.