Lord Coe helped London clinch the 2012 Olympics six years ago and was part of the bid team that won the rights to stage the 2017 World Athletics Championships.
Britain will also be hosting various other international sporting events in the coming years, but England's bid to stage the football World Cup ended in humiliating defeat last December when they were eliminated in the first round after the vote by FIFA's 22-man executive committee.
When asked why that bid failed where others from Britain have succeeded, IAAF vice-president and London 2012 chairman Coe told BBC Radio 4: "Because I don't think that English football has enough people of influence at the highest level of the game internationally, I've always sensed that.
"I think in track and field we clearly now do. I think in the Olympic world we clearly now do. But I think football doesn't really punch its weight in those corridors.
"I think we sometimes confuse the power and the global reach of the Premier League with influence in the corridors of power in the administration of the game, and I think that gap has got to close and I think between now and the next chance that we have to host the World Cup the FA's just got to figure out how to get people from the English game into more senior levels of influence in the world game."
Coe believes other sports have shown they are heading in the right direction in this aspect.
Asked what the World Championships success will do for Britain's voice abroad in international sport, Coe said: "I think that voice is coming stronger all the time.
"I sensed 30 years ago when I first got involved in sports administration that we had drifted well off the pace.
"We weren't really attracting big events and when we were bidding for them we were rarely succeeding. I think it's shown the world that when we actually do this well and if we bring the right people together and make the right case, that we do get across the line and sometimes against city and countries that bring greater levels of budget and funding to these campaigns."