Saido Berahino's 14th goal of the season settled a dour clash between two struggling sides at The Hawthorns.
The game looked destined to finish goalless until Allan McGregor picked up an Ahmed Elmohamady back-pass 13 minutes from time and Berahino rifled home the resulting free-kick from around 10 yards out.
He said: "The important thing is people have to recognise how tough this is going to be.
"People think I'm just saying it to take the pressure off, well just have a look at the Championship and have a look how many teams are in the Championship who have spent years in the Premier League.
"The reason why they've gone into the Championship is because they've got complacent. People around the place got complacent, without a question of a doubt.
"Everybody took their foot off the pedal and almost accepted that they were going to remain in the top flight and as soon as you do that you'll get relegated.
"This club and everybody around the club has got to understand that this is a real dogfight until the end of the season and for us to stay out of it, everybody has got to pull together. That's not just myself, the chairman, the staff, the players, but the supporters play an enormous part.
"They were brilliant today, very patient, they kept behind the players and we will need that from now until the end of the season."
