Reid quizzed Farage on whether he could guarantee the bold pledge promoted on the side of a much-photographed battle bus would be delivered on.
Farage responded simply: "No I can't," and added that it was a "mistake" of the official Vote Leave campaign to have made the claim in the first place.
Reid rebutted him saying: "Hang on a moment, that was one of your adverts".
Farage insisted that it was in fact a claim carried by the official 'Vote Leave' campaign, not his own party's 'Leave.EU', but still acknowledged it was wrong.
But Reid fired back that the pledge may have influenced a lot of people to vote Brexit.
She asked: "You're saying, after 17m people have voted for Leave based - I don't know how many people voted basis of that advert, but it was a huge part of the propaganda - you're saying that was a mistake?"
Farage responded that the contribution - which he said was more than £350m a week - could be spent on public services including "the NHS, schools or whatever it is".
The figure has been criticised repeatedly in the past for being "misleading", including by the UK Statistics Authority.
The Ukip leader defended his personal position, saying he had been "ostracised" by the official Leave campaign, adding: "As I've always done, [I] did my own thing."
Despite the apology, many voters expressed disappointment Farage's comments.
Chris Green, Scotland editor of the i newspaper, also bemoaned the pledge U-turn coming shortly after Conservative MEP and ardent Brexit supporter Daniel Hannan reportedly said that voters expecting a fall in immigration levels would be "disappointed".