The Dons lost 2-1 to Kairat Almaty in the first leg of their Europa League third qualifying round on Thursday, but they showed few ill effects of their 7,000-mile trip in getting their Scottish Premiership campaign off to a winning start.
“I’m absolutely delighted with everything, given the circumstances,” McInnes said.
“With everything we had to endure prior to coming here, the fitness levels, the strength and the determination was what we should be talking about.”
Aberdeen were backed by 3,500 travelling fans at Tannadice, and McInnes was pleased to see his players overcome any psychological fatigue to reward them.
“I always felt we would be fit enough. It was the mental side of it,” he said. “We couldn’t have tired minds, we had to treat the game as the first day of the season, that anticipation and excitement.
“Our fans were treating it that way and they deserved to see their team treat it the same way.”
“And I’m delighted for (goalscorer) Kenny (McLean) because I thought he was the best man on the park,” McInnes added.
But Dundee boss Jackie McNamara was not discouraged by their opening day defeat: “Aberdeen are favourites to finish second but I didn’t see a lot in the match,” he said.
“They have a strong squad but I have belief in my own players that we can have a successful season.
“I don’t think there were any real chances and I don’t think we deserved to lose the match.”