David Miliband told LBC's James O'Brien that those wishing to challenge Boris Johnson should focus on policy and not his "latest contradiction".
When asked if there were parallels with the way Donald Trump is treated by adversaries in the US Mr Miliband said that "focussing on the personal peccadilloes" distracted foes in both media from "the damage they're doing to the country".
"There's a Trump-denotation syndrome which is 'what's the latest thing he's said or the latest contradiction between something he said today and something he said yesterday'.
"In the end, the voters don't care about whether he's consistent, what they care about is whether he's delivering for them."
Mr Miliband added: "I think that's going to be a lesson in dealing with Boris Johnson, because there's going to be no shortage of contradictions, but he's going to laugh them off.
"The question is whether or not helping the country or damaging it.
"If you end up focussing on the personal peccadilloes you're not actually focussed on the damage they're doing to the country."