An injury-time penalty from Raphinha secured all the three points for the home side at Elland Road, leaving the visitors to rue a series of missed chances.
Christian Benteke, a second half substitute, spurned a glorious opportunity just five minutes after coming as he headed wide from close range. The Belgian had another opportunity late on, but Leeds keeper Illan Meslier stopped his shot just before it crossed the line.
Patrick Vieira was disappointed with his team's lack of cutting edge in front of goal
The manner of the defeat irked Vieira, who has seen his side lose twice within four days following a 2-1 loss at home to Aston Villa on Saturday.
'I’m frustrated because we were the better team,' the Frenchman said.
'When you don’t put away your chances, you know you can get punished.
'I don’t want to focus on the penalty. We had a couple of good chances, especially in the second half.