Craig Bellamy put the hosts in front at Old Trafford with a clinical volley early in the contest.
But Stuart Pearce's men were then pushed onto the back foot by the Africans' ultra-physical approach, which largely went unpunished by Uzbek referee Ravshan Irmatov.
Still, it did seem GB had weathered the worst until Konate struck eight minutes from time.
The hosts pushed forward frantically in search of a winner but they came no nearer than a Marvin Sordell effort that crashed against the bar.
And the greatest damage could yet be felt in the dressing room, with both Bellamy and Joe Allen needing to be checked after sustaining worrying knocks.
For all the doubters, who just could not get their head around the concept of a Great Britain team, even at a home Olympics, Old Trafford was still packed at kick-off.
There were even repeated chants of 'GB' rolling round the stands at regular intervals as the two sides engaged in some early sparring.
And when Bellamy became the first GB scorer at an Olympics since Northern Ireland's Patrick Hasty in 1960, there were genuine celebrations, both amongst the fans and, more importantly, the players, who have had three weeks to work together.
There was some justification for Stuart Pearce that all three overage players were involved.
First Ryan Giggs sent over a cross from the right, for which Micah Richards challenged.
It was Steven Caulker who got his head to it though, nodding it down for Bellamy, whose first-time finish flashed past Ousmane Mane and into the far corner.
Not that GB should have been in front for long.
After spending the early part of his summer gaining experience as England's number three keeper at Euro 2012, this was Jack Butland's chance to shine.
The 19-year-old almost blew it though, directing a routine clearance straight to Sadio Mane, who chipped disappointingly wide with only Butland barring the way.
It would be fair to say Senegal like a tackle. And Ryan Bertrand was not the only GB player to get up gingerly rubbing part of the body - in his case an arm - after being clattered.
The introduction of Bolton's Sordell for Daniel Sturridge at half-time was a worry, although not as much as Ibrahima Ba's shot that required a smart low save from Butland to keep it out.
A day before the action starts in the capital, Lord Coe was present, as were Manchester City's Joe Hart, Nigel de Jong and Joleon Lescott.
After signing plenty of autographs at half-time, that trio would doubtless have been impressed with Senegal.
Zargo Toure thundered a shot over before Saliou Ciss brought another decent save out of Butland and Rose cleared a powerful Abdoulaye Ba header off the line.
Joe Allen's exit after an hour was another cause for concern as he had already been down once, and then came another shocker as Ciss wiped Bellamy out on the edge of the area with a tackle that caught the striker around the knee.
Home players charged in to express their disgust, yet GB did not even receive a free-kick.
Bellamy was able to continue, although he was eventually replaced, to the kind of reception he has never experienced at Old Trafford before.
The uplifting atmosphere was punctured by Konate eight minutes from time as he delicately lifted the ball over an advancing Butland to deny GB their win.