Scotland beat the Croats home and away in their Group A qualification campaign but once again lost out with Croatia clinching their trip to South America via the play-offs.
The Scots have not graced the finals of a major tournament since the 1998 World Cup in France and the disappointment from another failed attempt returned when Regan took his seat in the Arena de Sao Paulo to see Croatia take the lead against the hosts before losing 3-1.
Speaking after the Scottish FA's AGM at Heriot Watt University in Edinburgh, where the national performance centre for sport will open in 2016, he said: "It was nice to experience a World Cup, I had never been to a World Cup before.
"FIFA held their congress there prior to the start of the World Cup so myself and the other 208 countries making up FIFA were part of that delegation and we attended the congress, the opening ceremony and the first game.
"When you are sat watching Brazil versus Croatia in the first game and you know that you have beaten Croatia home and away, you think 'if only' and that it could have been us.
"The atmosphere was fantastic. When Croatia went 1-0 up you could have heard a pin drop.
"When Brazil equalised, it nearly took the roof off the stadium.
"You could imagine what the Tartan Army could have been like if we had been playing Brazil and if we had gone 1-0 up in the Arena de Sao Paulo."
Regan believes the improvement Scotland have shown under Gordon Strachan means reaching the 2016 European Championship in France is a distinct possibility.
"We are going into the start of France 2016 (qualification campaign) knowing that we will never have a better chance," he said.
"Twenty-four teams can qualify for a major tournament. We are six games unbeaten, we have a manager who has instilled a sense of belief amongst the players, a manager who has made us very difficult to beat and who has brought in some fantastic young talent.
"So you, it does make you want it, it makes you feel that it is within your grasp."
Regan is well aware that the greatest football show on earth is taking place against a background of some controversy, not least due to the Qatar 2022 World Cup bid, which has been hit by a series of corruption claims which have prompted FIFA to begin an inquiry.
Lawyer Michael Garcia is leading an independent investigation into the bidding process for both the 2018 World Cup, to be staged in Russia, and the 2022 event.
Regan would support a re-vote on both bids if "there has been any wrong-doing".
He said: "If Michael Garcia's investigation proves that there has been any irregularities, then absolutely, I would support a re-vote and so would my board.
"It is not new. What has come out is more documentation and 'evidence' and that evidence is being explored by Michael Garcia.
"If it is proven that there has been something that has broken the ethics code of FIFA then clearly action has to be taken. It has to be transparent."
On the home front, it was agreed by Scottish FA members that, "any clubs seeking full membership are required to satisfy at least entry level club licensing criteria. In addition, from the start of season 2016/17, all existing members are required to maintain their club license in order to retain their full membership of the Scottish FA."
Among the other significant resolutions, the professional game board will be offered a second seat on the Scottish FA executive board.
However, a resolution designed to reduce the length of service required in official Scottish FA positions for potential candidates as office bearers was not approved, likewise a resolution to require all participants in the Scottish Cup to have a full license.