Taylor Rochestie led Göttingen for the second time this week with 25 points and five boards, with Chris Oliver adding 15 points for the Germans.
Only Nemanja Protic and Branko Lazic finished in double figures for FMP with 16 and 14 points respectively.
Jason Boone opened the scoring for the German team, and they led for most of the first period before a 7-0 run capped by a Chris McNaughton jump shot sent them into the first break 25-12 ahead.
A pair of Predrag Samardziski free-throws saw the hosts cut the deficit with the opening score of the second period, but Taylor Rochestie's trey made it a double digit lead for the visitors and they went into the locker room at half-time leading 42-28 as Rochestie again drained from downtown.
Göttingen still held a double-digit lead at the midway stage of the third period, but treys from Nemanja Protic and Bojan Radetic started an 11-0 run which saw FMP close to within a point going into the final 90 seconds of the quarter.
The visitors edged ahead again, but another Protic three-pointer cut Göttingen's lead to 56-54 at the final break.
Radetic levelled the scores with a pair of free-throws to open the fourth quarter, but although FMP stayed within three points for most of the period, they could never take the lead and Boone made it a two possession game 12 seconds from time with a dunk, before Rochestie wrapped it up from the line.
"We saw a good game where both teams gave their best. Both sides played good defense and FMP came back in the second half and caused us some problems. Basically one couldn't have guessed the outcome of the game until the end. I am proud of my team that they played with their heart for the whole game."
Taylor Rochestie, Göttingen player:
"We came here trying to get a win. We tried to stay physical throughout the game. We had to play as a team. Congratulations to my team."
Bosko Djokic, FMP coach:
"Congratulations to Göttingen! They are a good and organized team. I would also like to congratulate my team but only for the second half, as in the first half we looked very bad in defense. W definitely have to work more on our defense. We have to learn and work a lot. We will have seven days of preparations at Zlatibor to get ready for Super League."
Sasa Stefanovic, FMP player:
"Congratulations to Göttingen, they fought and gave their best. Unfortunately we couldn't qualify even though we had a chance tonight and in the first game. However, we have to concentrate now on the domestic league."