The mayor said he will instead be judged on his record over a range of areas, including affordable housing provision and his decision to provide free lunches to all primary school children over the coming academic year.
Mr Khan said Tuesday was a “landmark day” for the capital and he insisted that a “silent majority of Londoners” support the Ulez expansion.
“Whether it’s the free school meals that will start from next week, whether it’s cleaning up the air in our city, whether it’s the record number of mentors in our city, the record amount of investment in our policing, record numbers of affordable homes, record numbers of council homes.
“An election is fought on a number of issues - it’s not a referendum.”
Mr Khan’s Conservative opponent at the next election, Susan Hall, has pledged to scrap the expansion “on day one”, if she takes office.
The widening of the Ulez’s boundaries has been controversial since its announcement last year, as opponents have argued it will put a further financial burden on the poorest during a cost-of-living crisis. Drivers of older, more polluting vehicles in the city’s outer boroughs now face a £12.50 daily charge.
But Rosamund Adoo-Kissi-Debrah CBE, who lives in Lewisham and whose daughter Ella died from air pollution in 2013, said she felt “relief” at the expansion.
“My borough is now not divided,” she said, referring to the fact that Ulez was previously contained within the North and South Circular roads.
“There are children who live on the South Circular... They live right on it. Look at the windows as you go past, all the black spots.
“We have one of the highest rates of asthma in London, in Lewisham.”
Nine-year-old Ella was the first person to have air pollution listed as a cause of death at a UK inquest, after she died from an asthma attack.
Her mother said: “In the UK, 22-24 children die every year still from asthma - between eight and 12 come from London. If, at the end of the year, there are fewer deaths, I’ll take that.”
Non-compliant vehicles make up around one in ten of those seen driving in outer London on average, Transport for London (TfL) say.
Christine Calderato, TfL’s director of transport strategy and policy, meanwhile confirmed that warning letters may in some cases be issued to drivers of non-compliant vehicles, rather than immediately fining them £12.50 per day.
“We can issue those warning letters as a discretion,” she said.
“If we can try and understand if somebody’s made a mistake, then obviously we’ll always use that discretion.
“But we want to make sure that people know that the scheme is in place. As of today, you could be liable for a charge, so please do either pay your daily charge or sign up to auto-pay, to make sure that you don’t receive a PCN [penalty charge notice].”
Oliver Lord, who leads the UK branch of the Europe-wide Clean Cities Campaign, said the scale of the Ulez policy was “incredible”, but that there was still work to be done.
“Other cities across Europe are looking ahead - beyond diesel, beyond petrol,” he said.
“How do we start to incentivise people to transition to even cleaner, electric vehicles?
“That’s where I hope we can move the political discussion onto now, so long as the right support is in place, as well as just regulating.”
Louise Krupski, Lewisham Council’s cabinet member for the environment and climate, said the expansion was “fantastic” and that her authority had “hardly had anything” in terms of criticism towards the scheme from local residents.
Asked about the apparent difference in outlook on Ulez between Mr Khan and Labour leader Sir Keir Starmer, the Labour councillor said: “I think it’s difficult, I really do.
“We’re coming into a general election and I think it’s difficult when you have a controversial issue.
“I’ve always been very clear on my position, that we need to stand behind Sadiq, and this is a positive day for London.
“I think over time we will see that, and I think that that will be brought into the national scheme of things.”