He said the game's national governing body, which itself celebrates its 150th anniversary this year, was always considering ways to ensure the competition remained relevant, with the Premier League and the Champions League appearing to carry more importance for the biggest clubs.
"Our view is that there are absolute fundamentals in the cup and one of those fundamentals is the free draw," he said. "The absolute tradition around the ability of a club to be picked at home, away - against a big club or against a small club, we think tinkering with that would be a mistake."
The FA has not been afraid to make alterations where it has felt they were worthwhile - such as shifting the kick-off time of the FA Cup final to 5.15pm from its usual 3pm slot. But Horne was against making further inroads into the competition's traditions by seeding the draw, and also rejected the idea of scrapping replays, which has been proposed.
He added: "I think replays are an absolute part of the magic of the cup - if you look at the replays that were earned yesterday some of the big clubs have got themselves into a spot of difficulty having to go and play away."
Horne, general secretary since 2010, admits the competition has to change to appease fans and teams alike if it is to remain a major trophy.
"We talk regularly about ways in which we should look at the competition, what we are very nervous about is tinkering with it and potentially damaging it," he told BBC Radio Five Live's Sportsweek.
"You have got to recognise that the FA Cup needs to appeal to a new generation, it needs to stay relevant in a very different landscape to that which a lot of us remember historically."
One of the traditions which has been altered is the kick-off time for the final. Chelsea ran out 2-1 winners over Liverpool in a 2012 final that kicked off at 5.15pm in an effort to attract a higher television audience, something Horne reckons was a good decision.
He said: "(The) 5.15 (kick-off) worked really well for us. We had over 500 million people watch the game globally and 11 million people watched it domestically which was actually more than the Champions League final with Chelsea in it."