Horne was among representatives from five sports - football, cricket, tennis and the two rugby codes - who attended a summit with ministers in Whitehall on Tuesday morning for talks on tackling fixing.
It followed the arrest of six people, including Blackburn striker DJ Campbell, following an investigation into spot-fixing in football by the National Crime Agency (NCA).
Horne, who was at the meeting with culture, media and sport secretary Maria Miller, said the "general consensus" was that fixing was not a widespread problem. Representatives from the Premier League, Football League and British Horseracing Authority (BHA) were also present.
He insisted however that the FA took the issue seriously and will study measures against fixing already in place in cricket and horse racing.
Horne said after the meeting: "I think the general consensus around the room was this isn't a big issue. The intelligence that we have says this isn't a wide-scale issue at the moment but, again, we don't want to be complacent.
"It's clear that, as Britain, we are very proud of our sporting product, of the sport that we play in this country and we all want to do all we can to protect the integrity of that sport.
"We are never complacent on this issue and there's a lot we can learn from other sports. Some of the education programmes that cricket have put in place are very far advanced, and the integrity unit that the BHA have in place is very far advanced so there's lots of learnings that are open to all sports."
The FA has its own integrity unit and education programmes, but fixing has been an issue for a longer time for horseracing and cricket.
Horne added: "We don't want to see this in our sport and so, therefore, we are doing everything we can, we are looking at all measures we can across sport but also with the agencies.
"We really welcome the recent impetus from the NCA. I think that is going to be a really important body for all of us in reminding people that these are criminal activities and the criminal nature of activities shouldn't be underestimated and all power to the NCA."