The Frenchman's habitually serious face took on a foxy grin. "That was the case already," he said. "Being Arsenal. And having a fine manager. It was enough."
But while some things may come as no surprise to a man who has now managed sides to Cup wins in Japan, France and England, the enormity of what he has achieved in the 19 months since he arrived at Highbury from Monaco was taking some time to sink in.
"I frankly must tell you I don't really realise what has happened today," he said. "In September I would never have believed we could do what we have done. Of course it surprised me - if you play teams like Liverpool and Manchester United, how can you plan for the Double? That would be crazy. But you take success when it comes."
With his latest success comes the looming challenge of guiding Arsenal through the European Champions' League. Looming, that is, if you have a disposition such at Wenger's. "I started thinking about next season two months ago," he said. "A lot of the players are still very young, so we have to keep the older ones fit for next season."
Wenger, who has another year of his contract to run at Highbury, said he would be keeping all his current players, but had in mind signing two more before the World Cup gets under way next month to strengthen his squad for European matches.
Asked if one of the players under consideration was a forward who was good in the air, he replied, with a smile: "Good question."
The Arsenal manager indicated, however, that his England forward Ian Wright would be staying on to earn a place in next season's team. "I want to keep him at Arsenal, and he told me that he was happy to stay."
He acknowledged the palpable frustration which Wright - back in the running and hoping for a World Cup place after his long-term groin injury - had experienced as he waited in the Wembley dugout for a call to action. His frequent warm-up sorties down the touchline, while diverting for the Arsenal followers, proved ultimately futile.
"It was hard for him," Wenger said. "He was unhappy not to be named in the team but he was great about it. I couldn't bring him on because I didn't want to disrupt the organisation of the side. I think it's one more month before he will be fully fit. He has only had two games to prepare for a Cup Final."
The roots of this season's success, Wenger felt, lay in the analysis he had made of Arsenal's performance in 1996-97. "Finishing third was not a bad thing for us," he said. "Maybe if we had gone into the Champions' League this season we wouldn't have won the Double. But by last summer I knew that we didn't win the big games, and that was the main thing I had to do something about. The main thing about this season is that every big game we have played we have won."
One of the key factors in that change of events, he said, was the arrival of the winger whom many felt to be a risky signing when he paid Ajax pounds 7m for him last summer - Marc Overmars.
"If you look at our season, Marc has played well in all the big games. He has scored 16 goals as a winger in his first Premiership season. I don't think anyone else could have done that."
Many of those goals have been crucial - such as the one which gave Arsenal the 1-0 win at Old Trafford that most observers regard as the result which tipped the balance of the title race.
Wenger was determined to sign Overmars, even though many warned him that the knee injury which kept him out of the game for eight months had effectively ended his career.
"We had to have the knee checked, of course," Wenger said. "But I never had any fears for him. We had a very hard pre-season training and he came through it with no problems."
Wenger acknowledged that the 24-year-old Dutchman had taken some time to settle into English football. "He took a while to adjust physically to the pace of the games," he said.
"But he is a world class player. He has such pace. Every English club that plays against Arsenal has to think `How can we stop Marc Overmars?' And of course that leaves space for others such as Dennis Bergkamp, Ian Wright or Nicolas Anelka to become more effective."
It is a formidable challenge for any defence - be it English or European...Reuse content