Nemanja Matic scored the only goal of the Group G encounter in the 34th minute, with the Premier League outfit unable to extend their advantage as Sporting proved more competitive after the interval.
Silva bemoaned his side's slow start, but took some positives from a spirited second-half display.
"We did not start the match the way we wanted," he said. "Chelsea began strongly and we were not able to block the fast players they have up front.
"When we were beginning to level things up we conceded the goal due to a lack of attention at a free-kick.
"In the second half, we took some risks and created enough chances to get a draw that I think that would have been a fair result."
Goalkeeper Rui Patricio turned in an excellent display to keep Chelsea at bay for long spells, but confessed that he would have swapped his performance for a positive result.
"I would trade my performance for one victory," he added. "We wanted to win, we fought hard, but we couldn't achieve the result we wanted.
"We still want to go forward to the next stage, so we will prepare for the next game the best way we can, so that we can get the win."
Sporting now sit bottom of the group on one point, behind Schalke and Maribor who are tied on two after their 1-1 draw on Tuesday.
