Thompson's comments, revealed in minutes of a meeting of the Commons culture, media and sport select committee, come following stinging criticism of the deal for the BBC to show just half of each season's F1 races live on free-to-air TV from next year to 2018.
Some viewers have objected to Sky's new Sky Sports F1 channel on pay-TV being the only place to enjoy the full F1 season, but Thompson said that the arrangement will save the BBC £150m at a time of major cost cutting.
Committee chairman John Whittingdale MP said that the MPs had received a "very large postbag" of complaints from people about the arrangement and pushed Thompson on whether the BBC looked to strike a deal with a different broadcaster than Sky.
The director general responded by saying that it was the BBC's idea to share rights to Formula One as a way to retain its presence in the sport, while also making "savings that otherwise might have meant deeper cuts in other services".
"We know that Formula One has only fairly recently come back to the BBC; it has been very popular on the BBC. Secondly, we know that Formula One fans ideally do not want Formula 1 to be interrupted by advertising, because of the character of the sport," said Thompson.
"Nor, of course - for the subset of Formula One fans who do not have Sky subscriptions - would they, ideally, like Formula One to go entirely behind a paywall. I believe that the arrangements that we have reached offer very good value to the licence payer, and the experience of Formula One on the BBC will still be very rich."
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Thompson added: "The first Grand Prix next season, when this new arrangement starts - the Australian Grand Prix - will be live on Sky in the very early hours of the morning. There will be a 75-minute highlights package in peak time on the BBC, which we would expect to reach many more people than the live coverage.
"Talking about changing the arrangements in the existing contract and the extension of that contract, all I would say - and I have of course heard the arguments that perhaps this could have been picked up by another free-to-air broadcaster - is that what we have done has guaranteed that a very large amount of Formula One will still to be free-to-air to the British public for many years to come.
"Had we simply stopped the contract and decided to walk away from Formula One after that, there was a real danger that all of Formula One would have gone behind a paywall."
Channel 4 had made a last ditch bid to pick up the Formula One rights, according to documents released after the BBC-Sky deal was announced. Whittingdale therefore asked why the BBC did not explore a joint deal with Channel 4, which would have kept the sport completely free-to-air.
Thompson replied: "We were quite clear that, to get the economics to work for us, it was going to have to be a pay partner, and this was the only pay partner, credibly, whom we thought we could involve in it - indeed, a pay partner who had expressed interest in this very topic of conversation previously. It was an example of a free-to-air pay partnership, which is not by any means unknown in the market."
He added: "It seems to me that it was not required of us, and given that, in a sense, what we were trying to achieve on behalf of the licence fee payer was a significant saving, actually keeping the confidentiality of the process until it was clear whether the thing was viable and whether all parties to it - including, of course, the rights-holder - were happy, militated in terms of doing it the way we did it."
For its new Sky Sports F1 channel, Sky has mined the majority of the BBC's Formula One team, including lead commentator Martin Brundle and Radio 5 Live's David Croft.
The BBC has also proposed plans to reduce its spending on sports rights by 15% up to 2017, but Thompson feels that the corporation can still hold its own as a broadcaster of live sport.
"We have just, literally in recent days, lost our entire Formula One commentary team to Sky, and there has been, over the years, a regular traffic of sports presenters and commentators from the BBC to ITV, Sky and other broadcasters," he told the MPs.
"What the BBC attempts to do, again, is to get the best value and best impact from its sport. In the current year, we account for around 2% of all the hours of sport broadcast in the UK and 41% of the viewing.
"People still want great sport from the BBC, and the BBC is a surprisingly good and cost-effective way of getting sport to everyone, whether they have the ability to pay for it via a subscription or not."