But Villas-Boas maintains that he is still the right man for the job despite conceding his side "weren't good enough" at The Hawthorns. Chelsea have now won only three of their last 12 Barclays Premier League games and have slipped three points behind Arsenal in the battle for the final Champions League spot.
Villas-Boas said: "Will this result increase pressure on me? You have to agree with it. We are in the same position, fifth, but we are now three points behind Arsenal. It is a big, big disappointment. Every defeat Chelsea suffers piles more pressure on any manager."
He added: "Today is acceptable that pressure piles on a bit more. We have responsibilities to the fans and the club and we did not perform."
Villas-Boas insisted it would not help his position being given public backing from Chelsea owner Roman Abramovich.
He said: "I don't think so. At the moment we just have to go on with our job and everyone must do better, players and manager for sure on that one.
"We have to improve and there is no need for the owner to back us after such a poor display. Am I the right man for the job? Yes. I wouldn't have taken it if I didn't think that."
Villas-Boas conceded his side were second best in all departments with only Ashley Cole, who suffered a severely bruised ankle in the latter part of the game, escaping criticism.
He said: "We have a defeat which is badly taken because we were very poor on the day. We have to improve. This is bad. This defeat cannot be well taken. The only player at an outstanding level today was Ashley Cole. The rest of us all under-performed from management to the rest of the players.
"Full credit to West Brom but we weren't good enough on the day. They won every first and second ball and were far superior to us. It's a big disappointment and a poor, poor display."
Source: PA
Source: PA