The Ibrox side lost two goals in quick succession early in the first-half. They put in a spirited second-half display but lost another goal from a set piece. Tavernier sought to take the positives from a performance in Naples after what has been a difficult European campaign.
"We are obviously disappointed we lost today," he told BT Sport. “I thought we could take some positives out of that compared to the rest of the games we have played in this group. We let two easy goals in the first half then felt we had two big chances which could have levelled the game.
“I thought there were some performances in our team which have been really good. James Sands and Ridvan [Yilmaz]. I thought they had a really good game. We have got to take positives out of this game and build on that.
They took their chances and we conceded (from) a corner. That's the level we are playing at. Teams get chances and they normally stick it away and we need to learn from that.”
Rangers sit bottom of the group with five defeats from five but can still earn the consolation of dropping into the Europa League but it will require defeating Ajax by five goals in their final group game at Ibrox.
“Any game our objective is to win,” Tavernier said. “It’s our last game at home and we need to put a performance in for our fans and that’s what we will be looking to do.”
Perhaps more importantly is the league fixture at Ibrox this weekend as Rangers look to get back to winning ways when they host an upwardly mobile Aberdeen who rose to third following a win over Motherwell at the weekend. The last two outings at home have brought about performances deemed not good enough by the supporters with the team booed off.
"We have got to pick ourselves up," Tavernier said. “We have two days of rest. It’s a defeat but there were some positives in the game we can take with us. The energy we put in when we tried to play football throughout the 90 minutes, we've got to take that into Saturday. Another big game, lots of energy and we need to get three points.
“It’s a defeat but it feels like a strange one because there were some good individual performances and collectively as a team.”