Having fought back to level the score in the 53rd minute through Luka Jovic, the Eagles were left disappointed as goalkeeper David Abraham conceded an own goal late in the meeting to hand his opponents all three points.
The result has left Niko Kovac's outfit fifth on the Bundesliga table.
“We got back into the game superbly after the interval and deserved the equaliser," Boateng, who lasted for the entire duration of the game, said, as reported by his club's official website.
"We also had some good chances after that and were on top.
"The own goal is very unlucky because the ball was in the air for a long time.
"No one will be more annoyed than Lukas himself.
"The point would’ve been useful and would’ve been deserved too, but unfortunately we had a lot of bad luck.
"The opening goal was also deflected, otherwise Lukas might have been able to save it.
"We have to accept it now; the important thing is we bounce back.”
Frankfurt host TSG Hoffenheim in their next game on Sunday.
On personal note, the Bremen fixture was Boateng's 27th league appearance for the Eagles since signing a three-year deal last summer.