Stanton's historic blast came in his 644th MLB game -- and it was his first of the season, coming on his 31st at-bat. Stanton has also now homered in four straight games against the Mets, dating back to last season.
Unfortunately for the slugger, the Marlins let the game slip away for a 7-5 loss.
"Enjoy it later," Stanton said. "Three-and-seven [Miami's record] is the only record I know right now. Enjoy those when it's time for that."
Stanton didn't receive the historic ball on Thursday night but hopes it is retrieved.
The Marlins are one of the younger franchises in the Majors, beginning play in 1993. Stanton puts team marks in perspective.
"There's only, what, 30 of them," Stanton said, referring to all 30 MLB teams that have a home run leader. "That's good company to be with. Keep it going. Make it hard to beat."
Miami struck first Thursday off Mets right-hander Dillon Gee when Christian Yelich singled with one out and stole second.
With the count full, Stanton blistered his two-run shot to right-center, which landed in the Mets' bullpen, to give the Marlins a two-run lead.
Stanton's teammates had some fun with the slugger after the blast, giving him the silent treatment in the dugout.
Stanton made his big league debut on June 8, 2010, and he's emerged as one of the premier power threats in the game. In 2014, he paced the National League with 37 home runs, becoming the first Marlin to lead the league in that category.
Miami's top five home run list includes Stanton (155), Uggla (154), Hanley Ramirez (148), Mike Lowell (143) and Miguel Cabrera (138).
"What he's been able to do in just a short number of years is just amazing," manager Mike Redmond said. "He means so much to this ballclub. He's such a great teammate. It's fun to watch him go up there and hit. You know you've got a chance every time he's up there. I know that was a big relief for him to hit that home run. It not only gave us a lead, it helped relax him, too."