The Stamford Bridge outfit have won just three of their last 12 Premier League games and are in danger of missing out on qualifying for the Champions League for the first time since Russian billionaire Roman Abramovich bought the club in 2003.
While Chelsea were losing and the pressure was mounting on Villas-Boas, former manager Jose Mourinho said he was planning a second trip to London in a week.
"West Brom were superior in every minute of the game," Villas-Boas told the BBC after Chelsea lost to Albion in the Premier League for the first time.
"Our first half was very poor even though we had a couple of chances. We`ve not been good enough for quite some time.
"Our position in the league is fifth and that means something is wrong. The statistics say we don`t win enough so they are not numbers that make us proud.
"In football there is joy and pain and another chance and we have another chance against Birmingham City in Tuesday`s FA Cup fifth-round replay. But we will have to do much better than this if we want to go through."
Bookmakers William Hill quote Mourinho at short odds of 5-2 that his next job will be back at Chelsea and the Real Madrid manager`s planned visit to London will only crank up the media speculation of a return to Stamford Bridge.
Asked about his latest visit to London by reporters on Saturday, Mourinho replied: "I don`t have to explain my private life to anyone.
"Out of respect to my club, and because I ask the same of my players, I always inform the club when I go on a trip outside Madrid. I don`t have to ask permission from you or say who I have seen.
"I don`t have to justify myself to anyone. I`m going (to London) again on Monday and I don`t think I need to write a document to ask for permission."
Mourinho has also been linked by the media with the England and Tottenham Hotspur jobs.