Carlisle made the comments at the end of his 30-minute session with the media Tuesday during the Mavericks' exit interviews.
"Listen, I would like to say one thing about Miami if I could," Carlisle said. "I thought Erik Spoelstra had the toughest job in basketball with that team because of the way the team came together and because of the unbelievably high expectations."
They added to the hype with a news conference that had a party-like feel, during which James vowed Miami would win multiple titles.
The pressure on Spoelstra intensified after the Heat stumbled to a 9-8 start, including a 106-95 loss to Dallas Nov. 27. That led to a players-only meeting and speculation about Spoelstra's job security.
Carlisle, president of the league's coaches' association, was widely credited for outcoaching Spoelstra during the Finals, in which James struggled, particularly in fourth quarters.
"My hat's off to Erik and the job he did," Carlisle said. "It was extremely difficult, extremely trying. We went through a lot of difficult times before we got to our moment. Their time will definitely come."
Tim MacMahon covers the Mavericks for ESPNDallas.com.