A goal from Christian Panucci and a brace by Mirko Vucinic secured the win for Roma. Chelsea skipper John Terry grabbed a consolation goal for the Blues.
“I am delighted with the players,” Spalletti told Sky Sport Italia.
“Everyone worked hard, especially [Matteo] Brighi and [Simone] Perotta in the midfield.
“Perotta was particularly good as he kept on supporting [Daniele] De Rossi and he kept on at [John Obi] Mikel.
“This allowed us to play further up and hurt the opponents. I am delighted with the result.
“Everyone worked hard and played an excellent game.
“We have stayed together and united over the last few weeks and the club have always given us all the support and players like De Rossi and Brighi showed this tonight.”
