The Londoners remain third on the table but could lose that position depending on the result fourth-placed Tottenham record against West Ham United on Monday.
After Yaya Toure and Carlos Tevez scored in the second half to down Chelsea, manager Rafael Benitez said his players would continue to do everything in their power to stay in the Champions League placings.
"Always when you lose, you have to be disappointed," he said.
"This game was important for us, so I am more disappointed. We could have been closer (to City).
"We have to carry on to try to win our games and fight for the top four."