"We put in a fiercely focused performance and we never gave up against a great team," De Rossi told the Roma Channel.
"Chelsea have a huge amount of quality and they can win games like this with one chance.
"They played with great intensity and it wasn't easy to play an English-style game.
"A draw would have been important to us but we managed to play on a level with one of the top three sides in Europe.
"I think we are on the right track and the return of Francesco Totti is a great boost because he is a player of incredible importance."