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] Darron 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.''