With both teams headed for a 2-2 draw, the Eagles gave up all three points late in injury time as Michy Batshuayi struck to win it all for the Black and Yellows.
The result has seen Frankfurt fall back to fifth on the league table, two places behind Dortmund.
“We lost today because Dortmund scored one more goal than we did," Boateng said.
"It was a superb match that ebbed and flowed from one end to the other.
"We put everything into the game and the players deserve huge credit.
"Maybe we’re at fault for wanting to win the game.
"We made too many mistakes in the build-up to their third goal, but we’re a close-knit group.
"We play as a team and lose as a team.”
Dortmund opened the scoring early in the 11th minute when Marco Russ scored in his own net.
The Black and Yellows held on to the lead until 15 minutes to full-time when Luka Jovic scored to restore parity.
But things were level for only two minutes as Batshuayi scored against the run of play to put BVB 2-1 up.
Frankfurt responded again, thanks to Danny Blum, who slotted the ball into the net after Danny da Costa sent in a cross a minute into injury time.
At this point, it looked as though the spoils were going to be shared at Signal-Iduna Park, before Batshuayi struck again with virtually the last kick of the game.
Boateng, who joined Niko Kovac's outfit last summer, lasted for the entire duration of Sunday's fixture.