Milan's tally is bettered only by Real Madrid (15), and while they are in a decent position this campaign, 12th in the standings on 12 points, they are struggling to ensure they will be there again next season.
Conceicao took over from Paulo Fonseca last month, and although he won the Italian Super Cup, his side are still eighth in the Serie A standings, and lost 2-0 at Juventus at the weekend, ahead of their home tie against Girona on Wednesday.
"I think every game is different. It's true that being in the best club competition in the world is always a huge motivation," Conceicao told reporters.
"Big teams like Milan have to work every year to be there. In the league we are working to have the right continuity to be there once again at the end of the year.
"The jerseys don't play, the trophies on the pitch count for nothing. It's the players who go on the pitch. Not only in the Champions League, it applies to all trophies."
Milan could face Girona without their most impressive player this season. Christian Pulisic is the club's top scorer, with 10 goals, three of which came in the Champions League.
The American winger missed the game with Juventus with a muscle issue, and while he is in the squad, Conceicao is unlikely to gamble on the player's fitness.
"Christian is staying with us, we have training tomorrow morning, let's see how it goes," the manager said.
"I don't want to risk losing him for a month or two months. He could be on the bench but it's better not to risk it."
Milan supporters have often protested against the club owners this season, but Conceicao wants to see the fans get behind the team.
"They have to support us, they have to be the 12th man, or rather, the first. Without them, the club does not exist," Conceicao said.
"Without the soul of the fans there is no club. I will do everything, the players will do everything, but we need their support."
Girona are 30th in the Champions League standings on three points, and in a battle to make the top 24 which would mean a place in the knockout phase playoffs. A win would guarantee Milan a playoff place and they can still qualify automatically for the last 16.