After spending millions of pounds bringing in the likes of Samuel Eto'o, Willian and Christopher Samba, Anzhi's billionaire owner Suleyman Kerimov suddenly and significantly withdrew his backing less than two months ago.
It saw Anzhi's £116million budget reduced to as low as a reported £32million, leading to the sale of their star players and the sacking of coach Rene Meulensteen after only 16 days at the helm.
It means just months after aiming for domestic and continental success, they head into the clash with Spurs bottom of the Russian Premier League and without a win this season.
"They are radically different from what Anzhi built in these past years," Villas-Boas said.
"The changes are so radical and dramatic that you find it hard to recognise the team and the project they set out to do in the beginning.
"It looks apparent that staying in the league has become their priority.
"They've got one point out of the game against Sheriff so it's going to be a difficult game with difficult conditions.
"We don't want to come here and play with the competition - we want to be serious about the project in that way."
The Group K tie comes on the back of a controversial 1-1 draw with Chelsea on Saturday.
Jose Mourinho's side ended the match on the top but down to 10 men after Fernando Torres was sent off for two bookable offences.
However, the Spaniard should have seen a straight red card earlier in the match for scratching the face of Jan Vertonghen.
The FA will review the incident, which left visible marks of the Spurs defender who, along with Paulinho, has been rested for the trip to Anzhi.
However, as one of the match officials saw the incident, no action could be taken under FA rules against Torres, infuriating Villas-Boas.
"It's extremely difficult to know where to start," the former Chelsea boss said in the pre-match press conference in Ramenskoye, a town on the outskirts of Moscow.
"Obviously, it is almost a farcical decision. It doesn't matter to me which player or club is involved.
"Neither do I want to, with my words, put into question Fernando's integrity; neither their manager's, in trying to defend what is our position.
"I think the FA has made a decision almost a joke. It looks incredible.
"How can you see the images, pretty clear, and come out without punishment, on something (which) overtakes all professional behaviour?
"I think the decision is a disgrace. If the committee can't solve such clear images I don't think it sets out a good first example and we're not asking nobody to retract themselves; the player to retract themselves. That would not be fair.
"This is a competition and in the end they came up with what they thought was fair for that.
"We don't want Fernando suspended because it can make them weaker, because their bench is so strong, but I think the FA has lost all opportunity to put some sense into the images everybody saw.
"I'm extremely grateful for ex-refs to be able to enlighten people a little bit more, though I think most of you guys saw the incident as something that is not tolerable in football."