In the aftermath of Saturday's match, the Portuguese tactician described the game as the Blues' worst performance of the season, and could do little to hide his disappointment.
Chelsea dropped a place in the league standings to fifth, after Arsenal usurped them in the Premier League race for that all-important fourth spot with a 2-1 win away at Sunderland.
Villas-Boas insists that the players will strive to improve, and says that he has sympathy with the club's travelling supporters who watched their team's poor showing against the Toffees.
"It is a normal reaction and fans have the right to demand from the manager or demand from the players," he told the club's official website. "If there are people who are always right, the people who are always right are the fans.
"They aren't the professionals in football but they are the people we respect most in the game. Their opinions are highly valuable.
"In defeat I have to take all responsibility and will take it for sure. So I will reflect hard on my preparation of the game and the things that I did to try to win the game."
Sky Sports reports suggest that Villas-Boas met with owner Roman Abramovich on Sunday after the club cancelled a planned day off. There is a full week for training ahead of the visit of Birmingham in the FA Cup before the Champions League knockout stage starts with a visit to Italy.
The next few days are going to be important for the outcome of Chelsea's season.
"In the end I am not in doubt about the commitment of the players," Villas-Boas continued. "It is disappointing to be in this position and we have to work to improve. The only thing that we can grab onto is our competence and our work.
"We continue to promote the players' best qualities and it comes with work and it comes with a positive attitude, not a negative one.
"Last week we were 3-0 up against the champions and the Champions League finalists and with a bit more competence we would have been able to win that game, so we are there and we have to continue to work."
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