"He's just one of those all-time great horses", said Baffert, who won the Triple Crown three years ago with American Pharoah.
The chestnut colt became the second undefeated horse to sweep the Kentucky Derby, Preakness and Belmont, improving to 6-0 in a racing career that began on February 18.
Bob Baffert became only the second trainer in history to win the Triple Crown twice.
Baffert - who has won more Triple Crown races than anyone - complimented his team for helping the horse, which ran three major, testing races in five weeks.
An hour after his historic win aboard Justify, jockey Mike Smith sat in front of a crowded room of reporters, describing what it was like for an "old man" of 52 to finally win a Triple Crown.
"It was a monster race", said trainer Dale Romans, trainer of seventh-place finisher Free Drop Billy".
"To me, Abel Tasman and Hopportunity, when they set the stage early, I thought this is going to be good, " Baffert said. He raced three more times after the Belmont Stakes, capping his career with a resounding victory in the Breeders' Cup Classic. It's a couple furlongs longer, also, than the Kentucky Derby, which to this point is the longest race that Justify has run.
Justify, who did not race as a two-year-old, is now undefeated in six starts.
Justify defied all the odds on his way to achieving Triple Crown immortality.
The morning after the Belmont Stakes questions quickly turned to what's next for the newest Triple Crown victor.
In the hours before the race, Justify rested in Belmont's Barn 1, across the street from a Wendy's, undistracted by the beer-soaked fans who reveled close by - including one who almost relieved himself on a tree.
"This means everything to Glennwood", said John Gunther.
The Belmont Stakes has already seen a Triple Crown victor within this decade, as American Pharoahsealed the deal in 2015.
"I believe there's just a flow that guides me and when I follow it, wonderful things happen", he said.
After a 37-year drought, Baffert and the crowd celebrated a cathartic win for American Pharoah in 2015. He said: "I'm so happy for Mike Smith, there's no one more deserving than him". I tell you, it's just awesome. I got very emotional, because I really think - I'm getting help upstairs.
"I wanted to see that horse's name up there (with the other greats) because we know he was brilliant from day one", Baffert said.
He had every reason to be thrilled that he had won the Triple Crown along with a legendary horse.