Villas-Boas, whose side slipped out of the Barclays Premier League top four after a fourth game without a win, was even goaded by his own fans during the 2-0 loss at Goodison Park, with visiting supporters chanting 'You don't know what you're doing' when the Portuguese substituted Michael Essien in the second half.
Villas-Boas, whose predecessor Carlo Ancelotti was sacked at the same ground last year, said: "I think today was one of our worst games of the season, if not the worst."
He added: "In our performance today we are short of anything positive. It is a difficult day for us, we take out a lot of negatives from this game."
Speculation over Villas-Boas' future has increased in recent days with Chelsea owner Roman Abramovich twice visiting the club's training ground, but he claims that did not affect the performance, and said: "You don't expect any effects from that."
The Portuguese was also unmoved by the negative chants against him and claimed he could understand some of the frustration, adding: "It is part of the job. At the moment we are sitting fifth in the league and it is not enough for us."
Everton took the lead after just five minutes when Steven Pienaar, making his first home appearance since rejoining the club last month, while the hard-working Denis Stracqualursi doubled the lead 18 minutes from time.
The victory was their third in successive seasons over Chelsea at home and maintained their recent revival, and manager David Moyes said: "That was a great result for us. There were good parts of the performance as well but the strange thing is I think we can play much better.
"I think we will play better once we get more confidence as the wins take us a long. We got off to a great start with an early goal, which gave us something to hang on to, but we wanted it.
"We had to ride our luck on a couple of occasions but in the second half we didn't look like we were going to concede."
Source: PA
Source: PA