James Watt and Martin Dickie applied to go on the show in 2009, after BrewDog had been running successfully for two years.
The duo got through the initial application process and were selected for a screen trial in Manchester.
James explained: “Martin and I put on our best clothes, practised our presentation and drove down to the BBC studios where we pitched our hearts out during the screen trial and thought we did quite a good job. However, the producers did not.
“They thought our business wasn’t a good-enough investment proposition for the Dragons and that BrewDog was not unique enough, or with enough growth potential to make the grade and appear on the show.
“Our pitch would have seen us offer the Dragons 20% of BrewDog for a £100,000 investment. Had any of the Dragons invested, that £100,000 would now be worth £360 million.
James added: “We now have a community of over 75,000 Equity Punk investors all over the world who are the heart and soul of our business.
“The Dragon’s loss was our amazing Equity Punks’ gain.
“Since then, we have gone on to build a pretty neat little business which is currently valued at £1.8 billion and which has raised over £250m.”