What Mansell didn't say is that the vast majority of carbon emissions that are associated with F1 are not produced by the cars themselves. They are produced by fans driving to the races, and from the electricity needed to watch the races on TV. If the teams are guilty of anything it is the amount of air travel needed to transport all the people and kit needed at each race (some of the teams are looking to address this by taking more budget airline flights).
The carbon emissions produced by the F1 cars themselves are minuscule in proportion to fan's emissions, and so in this respect F1's total emissions are probably *smaller* than, say, football's total emissions.
Take for example the English Premiership which has 20 teams, the smallest stadium is Fratton Park in Portsmouth, which has a capacity of 20 000. This means that for the Premiership (if we take the smallest stadium as benchmark) has approx 400 000 people watching each weekend. There are 38 weekends of Premier League football, meaning 15.2 million people watch football live every year.
The largest circuit in F1 (which I'm pretty sure is Yas Marina) has seating capacity of 40 000, there are 17 races each year. This means approx 680 000 people go to watch F1 live each year.
As you can see these are *very* rough estimates, but even with the lowest estimate of football's attendance and F1's highest attendance there are far more people driving to football than F1. This doesn't take into account TV's carbon emissions or many other factors, I admit, but it does give a rough estimate.

Just a quick note regarding the largest F1 circuit, you say Yas Marina, but that is in fact one of the smallest. Silverstone, for example accommodates 100,000 fans on an F1 weekend, and usually sells out.

But otherwise some good points :)

You know what I've just had exactly the same conversation with my Dad - I still think my points are valid. I didn't include any of the fans driving to Championship, League One, Two, La Liga etc etc