Scotland will take a six-game unbeaten run into the opening Euro 2016 qualifier in Germany in September and Regan was upbeat about the prospect of reaching that tournament to end an 18-year absence from major finals.
Regan did temper his enthusiasm in acknowledgement of a qualifying group also containing Poland, the Republic of Ireland, Georgia and Gibralter, but he did not disguise his admiration for Strachan as the SFA party returned from London yesterday after the 2-2 draw against Nigeria at Craven Cottage.
Scottish confidence has soared on the back of half-a-dozen fine results: a 2-1 win in Macedonia, a 2-0 home win over Croatia, a 0-0 home draw with the United States, 1-0 friendly wins in Norway and Poland, and the Nigeria game. Scotland's Fifa world ranking has risen from 69th to 22nd since Strachan took over at the start of 2013.
"Gordon has the whole country smiling again as regards the Scotland team and that is terrific," said Regan. "We are delighted Gordon has turned things around as quickly as he has and he has got the confidence of everybody that he is working with. You could sense at Craven Cottage the strength of feeling from the supporters. The atmosphere was amazing, the best I've experienced since I joined the Scottish FA."
Strachan's record over the 2013/14 international campaign was four wins, two draws and two defeats from eight games. He lost Kenny Miller to retirement from international football and gave debuts to Ikechi Anya, Gordon Greer, Andrew Robertson and - two nights ago - Derby County pair Craig Forsyth and Chris Martin. Regan said Robertson had been emblematic of the renaissance under Strachan.
"You can't believe he was playing for Queen's Park 18 months ago and selling programmes at Hampden. He's been a fairy story and Gordon has turned things around in every department. We're a completely different team from 12 months ago.
"We brought Gordon in not just for the end of the last campaign [he was appointed during the 2014 World Cup campaign], but for the Euro 2016 campaign. We felt that if we managed to turn things around and get ready for that it would be a real bonus. But, to be honest, Gordon has surprised everybody by how quickly he has managed to stabilise the ship and turn us into a side which is very difficult to beat. He is ahead of timescale in terms of what we would have expected by now.
"It's important to manage expectations and not immediately decide we are going to be the next European champions. If I have learned one thing, it is not to get carried away and let's not forget we have a very challenging group. You expect some really difficult games in the section against the likes of Republic of Ireland, Poland and, especially, Germany.
"But Gordon understands an awful lot about the players and we should never forget his network and understanding and knowledge of others. Watching teams and working with TV, he has an encyclopedic knowledge of players and teams and that is going to help us enormously in the Euro 2016 qualifiers.
"Gordon is very funny. His one-liners are hilarious. Everyone is smiling, but he is quiet in many ways. He's not in your face and larger than life, knocking on your door. Gordon has worked with the players at his disposal and what makes it even more impressive is that he's not been building a squad for years.
"He has done a remarkable job with players who are not big prima-donnas. We have guys in the Scottish Premiership, the English Championship and one or two from the Premier League and he has made them into an impressive unit. We are difficult to beat and have competition for places all over the pitch. We are all genuinely excited about Euro 2016 starting, without wishing to run away with ourselves."
Meanwhile Regan revealed that the "integrity hotline" created by the SFA in January - allowing anyone with information on suspicious conduct around match-fixing, immoral betting or doping in the game - had not raised a single issue. The SFA launched its "Keep It Clean" anti-corruption campaign and Regan happily revisited the topic yesterday after the suspicions raised by the National Crime Agency before the Nigeria game. Those suspicions were not on Scotland and the game passed without any suspicious betting patterns.
Regan said he was as confident as he could be that the Scottish game was clean. "We have been looking at this area for some time. UEFA are very keen the associations invest time and resources in knowing what is going on and that we have a clean operation within out own areas.
"There has not been a single incident which has needed to be brought to their attention. Not a single call," Regan added.
"We've taken a view we need to communicate, but what is encouraging is that, when things were going on last weekend, no-one ever pointed a finger at Scotland. While you are never totally confident we have a clean operation, we are as confident as we can be."