Boston captured the winner-takes-all matchup to claim the best-of-seven Eastern Conference finals 4-3 and secure a place in the championship series, which begins Thursday in San Francisco, AFP reported.
"We aren't satisfied. We've still got a long way to go," Tatum said. "We know we have a tough task ahead. I'm looking forward to it."
The Celtics, who eliminated 2021 NBA champions Milwaukee Bucks in seven games, led from start to finish but had to hold off a Heat fightback in the dying minutes to reach their first NBA Finals since 2010.
Boston advanced after losing the conference finals three times in the past five seasons.
"To get over the hump with this group, it means everything," Tatum said. "Not a lot of people believed in us, but it worked out."
Tatum, who also had 10 rebounds and six assists, was named the Eastern Conference Most Valuable Player.
"It was the biggest game of my career," Tatum said. "Going through those tough times helped us grow, helped us learn. They kept coming at us. We kept responding. We left it all on the floor. We got it done."
Marcus Smart and Jaylen Brown each added 24 points for Boston while Jimmy Butler led Miami with 35 points in a losing cause.
Miami, the East's top seed, missed a chance at a second NBA Finals trip in three years and a first title since 2013.
Golden State split two games with the Celtics in the regular season, winning 111-107 in December at Boston and losing 110-88 in March at home when star guard Stephen Curry was injured.
Boston hadn't been to the finals since losing 12 years ago to the Los Angeles Lakers. The Celtics haven't won the NBA crown since 2008.
The Warriors, in the NBA Finals for the sixth time in eight years, seek their fourth title in that span and the first since 2018.