Konate's 82nd minute leveller spoiled Great Britain's party as they hoped to start with a win after returning to Olympic Football tournament since 52 years as Craig Bellamy scored the first goal for the hosts to give them a 1-0 lead until the 82nd minute.
Britain fought hard to get the second, as they almost grabbed a winner when substitute Marvin Sordell struck the woodwork two minutes from time, which was just a failed attempt as Senegal held on for a share of points after a Group A encounter.
It was indeed a bruising encounter for the hosts as they dominated for a long time, while they were denied a penalty in the 70th minute after goalscorer Bellamy who was clattered in the area in an atrocious challenge by Senegal defender Saliou Ciss.
Though Great Britain started slowly, they took the mid-way through the first half with Ryan Giggs and Bellamy's contribution.
The Manchester United veteran Giggs, at 38 became the oldest man to play in the Olympic Football competition, swung in a curling cross from the right flank which was met by Steven Caulker's head and parried kindly for Bellamy who slotted home a cool finish.
Soon after that Senegal could have equalised however a blunder from Jack Butland let in Sadio Mane as Butland's mis-hit clearance went straight to Mane. But the striker's effort drifted disappointedly wide to spare the Bristish goal keeper's mistake.
After an open second half, Senegal were fortunate enough to get the goal in the 82nd minute to deny the hosts a win and a winning start on their return to the Olympic football tournament after 52 years.