Villas-Boas last week admitted his "project" was not backed by all of his players after reports emerged he was openly challenged by some of them during a training-ground summit eight days ago.
However, Sturridge claims Chelsea are "a family" and will prove it during what could be a season-defining fortnight.
"We are all together as one and we are not a divided unit," he told Chelsea TV. "We are a family and we've got a good unit going here and I think maybe we will see that in the next few games."
Chelsea are currently on course for their worst season since Roman Abramovich bought the club and need a positive result in Tuesday night's Champions League last-16 first leg at Napoli to ease the pressure on Villas-Boas.
Saturday's dire 1-1 FA Cup fifth-round draw with Birmingham extended their winless run to four games and Sturridge said: "I don't think it is a defining week for the club but hopefully we don't get in the same situation as against Birmingham where we have to come from behind."
He added: "They have some great individuals as well as a good team but we have the same and we are not going to worry about what they have got.
"We have to go out there with the attitude that they have got to worry about what we have got. I am certainly not worried about that and we are going out there with the state of mind that we can win the game and play some good football, maybe get some more opportunities and put them away."
Sturridge, whose 11 goals this season make him the club's joint top scorer with Frank Lampard, insisted Chelsea were doing everything possible to turn their season around.
"We are working hard in training and the standard has risen since the last couple of games," he said. "We know what we have got to do and we are not losing sight of that."
Abramovich has been more patient with Villas-Boas than any of his previous managers.
Avram Grant, who was sacked despite leading Chelsea to their one and only Champions League final, told talkSPORT: "My advice to Andre is to do his job and try to win games. What will happen will happen.
"In the old times, Roman didn't have so much patience. Now, I think he learned something and he has patience - I don't know for how long. It's more important for a manager to know that we are in a job where any day could be your last day."