Mancini blamed himself for his side's 1-0 defeat at Goodison Park on January 31, claiming: "I didn't prepare well for this game. I thought it was maybe easier."
Despite winning a Carling Cup tie in extra-time there earlier this season, Chelsea do not have the best record at Everton, not winning in the league since 2008.
And Villas-Boas insists he will ensure his side are fully prepared as Chelsea look to keep the distance between themselves and the chasing pack.
"We never underestimate Everton because our record at Goodison Park is not impressive," Villas-Boas said.
"It is a difficult place to go, and a team that has made a great transfer market without a lot of noise, but with the right buys.
"It is fantastic to see [new signing] Darren Gibson playing more often because he is a player of immense talent and Landon Donovan coming back to a place he knows well.
"I think the additions they made were fantastic, improving them a level and making them even more difficult to play against."
David Moyes is the third longest-serving manager in the top flight behind Sir Alex Ferguson and Arsene Wenger, approaching 10 years at the helm.
Villas-Boas has been impressed from what he has seen this season and feels the Toffees are heading in the right direction despite testing off-field issues.
"They have improved a lot from when we played them first [this season]," he said.
"Everton are always a solid team and can create problems, plus the environment of Goodison Park is never easy.
"Their situation in the league at the moment is 11th, but very close to eighth place, which will straight away change the perspective."
Villas-Boas admits the disappointment of Sunday's 3-3 draw against Manchester United at Stamford Bridge, when they had been 3-0 up, still lingered at training this week, which was overseen by interested owner Roman Abramovich.
Referee Howard Webb awarded what the Chelsea manager viewed as soft penalties which Wayne Rooney converted to give the Red Devils hope before substitute Javier Hernandez snatched a point six minutes from time.
Villa-Boas felt Danny Welbeck had simply tripped over the leg of Branislav Ivanovic rather than an intentional foul being committed.
The Chelsea boss said: "It is frustrating seeing a penalty like that given - there must be a new rule set out, we have them for two-footed tackles, now we [must] have to have them for players who stand out their leg on purpose, clipping the leg of a defender on purpose to fall to give a penalty.
"On the same weekend, we had two incidents of that from [Manchester City winger] Adam Johnson and Welbeck.
"So there needs to be a new rule for penalties when the attacker purposely sticks his foot out to dive for a penalty."