AVB pointed to Manchester United's difficulties at the Hawthorns last week when discussing the win.
"Man United had the same problems against West Brom," said Villas-Boas.
"Of course we are looking for the full performance for 90 minutes and we are confident that it will happen. Today was important for us to get back to winning habits and we did it by showing a great performance in the second half.
"Our public wants us to be champions and we are listening to their demands but we need their support all the time.
"Everybody must get involved and you must feel the presence of the public in a supporting way, not that they weren't, but you need full support, a good environment, good commitment from the public and good empathy.'"