Chelsea v Birmingham preview
Drogba's contract expires in the summer and, with no agreement yet reached, talk is gathering pace that he could be on his way in the summer.
Villas-Boas admitted during his press conference on Thursday that he had lost the backing of some of his squad but indicated that underperforming players may follow Nicolas Anelka and Alex out of the club in the summer.
"If the players want to be part of this club's future, they have to support the project with their performances," Villas-Boas said. "If some of them don't support me, that's normal.
"Two players have already left and there will be further departures in the future. Contacts will have to be addressed and changes will be made. We have to defend the Chelsea badge, because they don't pay us to be a failure and everybody understands the demands to be successful at this club.
"You don't contemplate rewarding people who under-perform in any football team and our objective now is to get the best possible position in the Premier League and continue to fight for two trophies. In the situation we are in, we have to demand we do a lot better. We really need some results to put us back on track."
Drogba, who has been accused of undermining managers at Chelsea in the past, insists he has every respect for Villas-Boas and that the players must take responsibility for the team's struggles.
"For me the manager's age is not an issue," he said in The Sun. "You have to respect his position and his authority.
"He came with his philosophy, which is playing a bit more football than the other managers. That's how he succeeded in Porto so he wanted to do the same at Chelsea.
"You know how it is when you come with a lot of ambition and it doesn't go the way you want - it's difficult. It's not easy for him but he's not the only one who is responsible. We all are.
"In football, everyone blames the manager first, which is difficult for him because he is on the sidelines when we are playing, but I guess that's football. It's difficult because we are trying to change the way we play and to adapt to his philosophy so that's maybe why it's taking time and we are struggling to be in the top two, but I don't think it's about the style the manager wants to bring to the team. It's about winning games."
He added in the Daily Telegraph: "He is trying to motivate the players. He is a good motivator. Training is good - it is not that different from what we were doing the previous season. He's ambitious; he wants to win, to succeed, to be successful in the Premier League.
"Talking in generally, not about Andre, a manager is the manager and he knows he's responsible for the wins and the defeats so he will be the one to be blamed first, but sometimes it's more complicated than that."
On his contract negotiations, he said: "We are still talking about it. Everybody knows I love the club, everyone knows I want to stay so we are discussing it and let's see what comes out of the discussions.
"I'm optimistic it can happen but at the same time if it doesn't happen that's life. But you will never change the respect and the love we created together. My heart is blue."