The Serie A side finished third in Group C after falling to a 1-0 defeat to Liverpool at Anfield on Tuesday.
Koulibaly felt Napoli were so close to producing a huge surprise by advancing from a group that also included Paris Saint-Germain.
"We were so close. When the group stages started, many people saw us already out of the Champions League," he said.
"We are very sorry because we could have surprised everybody and we couldn't do it.
"We have a good team though and I know we will have many good moments in this season."
Napoli finished third in the group, dropping them into this season's Europa League.
"We will have to give everything in the Europa League to go as far as possible, and even try to win it," he said.
"We know it won't be easy because now we are the favourite for it. It will be a difficult competition because there are good teams in the Europa League.
"But we have time to think about it, now we must think about tonight. We will try and win it."