The Team Shoe-Box fighter gave all he had in the 10-round contest, but the ringside judges awarded the fight to Frenchman Cissokho who takes Conway's WBA Intercontinental super welterweight title.
The bout was on the undercard of the huge Canelo Alvarez versus Billy Joe Saunders world title fight at the AT&T Stadium in Arlington, with the event broadcast live across the world on DAZN.
It was a competitive fight in front of a record crowd of 73,000, but Cissokho appeared to be edging it as it entered the closing stages of the fight.
That nearly all changed in round nine when Conway landed a big shot that sent the Frenchman crashing to the canvas.
But the 2016 Olympic bronze medalist was able to get back up to his feet, although he managed it agonisingly close to the 10 count.
The fight ended up going the the distance, and it was Cissokho who secured a tight points win, with the judges scoring it 97-92 Conway, 96-93 Cissokho, and 95-94 Cissokho.
The defeat was the second in Conway's professional career, and his first in any fight scheduled to last more than three rounds.
The 25-year-old now has a record of 16 wins, one draw and two defeats from 19 bouts.
The main event saw Canelo beat Saunders, claiming a win by TKO after eight rounds.