Sporting's defeat - coupled with Schalke's 1-0 win at Maribor, also on Wednesday - eliminated the Portuguese side from the competition.
That disappointed Silva, who clearly felt his side had done enough to reach the last 16 of the Champions League.
"We did everything in all six matches to go through to the next stage," Silva said.
"We knew this was always going to be a very complicated match and there were times when we were not as aggressive as we should have been.
"We did not start the match the way we wanted and the way a match like this demands.
"We deserved to be in the next phase for all we did in this group stage, but that did not happen and now we will have to follow our path in another competition."
Sporting captain and goalkeeper Rui Patricio acknowledged he was upset with the result but that his team could be confident about a strong UEFA Europa League campaign.
Sporting drop into Europe's second-tier competition after finishing third in Group G, four points ahead of Maribor.
"We gave everything but we were not able to get the point we needed to go through to the next phase," Patricio said.
"This is football. Now we head to the Europa League to give our best.
"We go out of the Champions League with our heads held high.
"We are sad with this result but we will go to the Europa League searching for wins."
