Ben Mockford had the hot-hand all night and converted a superb five triples on his way to an eye-catching 19 points, but it wasn't quite enough to take down the home favourites as Great Britain were once again denied victory in a hard-fought clash which could have swung either way.
With Mockford providing the offensive firepower in the backcourt and Kieron Achara having yet another very efficient game in the paint and eventually collecting 13 points from a classy five of six floor-shooting display, Great Britain had Bosnia and Herzegovina sweating right until the closing seconds.
Apart from a wobble either side of the interval, Joe Prunty and his team were generally very effective in keeping pace with their opponents and had competed strongly during the early exchanges with a 'and-1' play by Myles Hesson putting them 7-5 ahead.
While a perimeter score by NBA star Mirza Teletovic put the hosts 22-19 in the lead at the end of the first quarter, back-to-back scores by Achara and Mockford at the start of the second period witnessed Great Britain move back in front.
Bosnia and Herzegovina then shifted up a gear with an explosive 17-4 burst of scoring, but Great Britain responded with ten of the last twelve points in the half, including three-pointers by Achara and Drew Sullivan - either side of successive buckets from center Eric Boateng to claw their way back at 41-37.
There was a sense of déjà vu after the action resumed as the local side firstly soared back into a commanding lead at 55-44, but yet again there was real spirit from Great Britain, who showed immense pride and poise to haul themselves back into contention with a stunning passage of play.
GB outscored Bosnia and Herzegovina 19-8 either side of the third and fourth quarter break with some excellent basketball, including a pair of triples from Mockford and ultimately a score by Achara which put Great Britain on a level footing at 63-63, which set up an exciting conclusion.
With Teletovic around, Bosnia and Herzegovina had someone capable of taking the game away and after consecutive downtown scores, it looked like he had put the contest out of reach, but Great Britain showed resilience.
Achara and Mockford continued their stellar work and combined for another inside score and triple to get within a point at 69-68, but the visitors couldn't sustain their momentum during the last few minutes as Bosnia and Herzegovina upped their defence and executed the plays needed to edge across the finishing line.
Boateng and Kyle Johnson also recorded double-digit scores by sinking 11 points and 10 points respectively for Great Britain who finished their campaign with a hugely positive performance. A full set of game statistics is available here.
It has been a challenging programme for head coach Joe Prunty and he explained that while disappointed at not meeting the team's ambition of another place at EuroBasket Final Round, he couldn't have asked for more in terms of effort.
"We had a specific goal in mind and we didn't achieve it which is unfortunate, but my guys really did give everything as a team," Prunty told gbbasketball.com
"I am proud of that effort and especially since we had some knocks and injuries, but everyone battled through those and never stopped fighting.
"Obviously, results were not what we had been searching for, as we wanted to qualify for EuroBasket 2015 and now we have to take time to reflect and evaluate."
"I knew the guys would play with pride in this last game and it was positive to see Ben (Mockford) play great and other players like Eric (Boateng) step up.
"Ben, in particular, deserves a ton of credit for being such a great team-mate and working so hard. Especially with it being his first year with the team and only being fresh out of college - he can be proud of himself."