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.
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 as one way to alleviate fixture congestion and make a winter break workable.
"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.
"I think replays are an absolute part of the magic of the cup - if you look at the replays that were earned yesterday [Saturday] 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: "We need to be pro-active, you remember in 1983 there was no football on a Sunday, things change all the time. "We are trying to appeal to new audiences all the time and move with the times - no longer are people finishing work at lunchtime on a Saturday.
"(The) 5.15 (kick-off) worked really well for us from a broadcast perspective, from a new audience perspective. 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."
This season's showpiece final will kick-off at the slightly later time of 5.30pm but Horne does not envisage a Saturday night final any time soon, and thinks Sunday finals could be difficult from a transport perspective.
"(The later kick-off time gave us) great audiences, a great way to appeal and a great way to keep the magic of the cup alive," Horne added.
"I have to say that (5.15pm or 5.30pm) feels about right, much later than that and you are going to cause a problem for the travelling fans and that is the last thing we want to do.
"It (Sunday) is a possibility, it would be a balance for the fans travelling and the audiences enjoying the game at home.
"My instinct is that Sunday gets a little more difficult for transport arrangements, it is not something we have thought about."