A Chris Brunt strike and Rob Green own goal saw the Baggies claim a 2-1 victory at Loftus Road, with striker Djibril Cisse's late consolation not enough to prevent the West London side from returning to the foot of the Premier League table.
The result prompted further criticism in Fernandes' direction, but the Malaysian has called on fans to back the team as it looks to avoid the drop in the second half of the season.
"Reading some of the rubbish on Twitter," Fernandes said on the social networking site. "[The] club is being rebuilt. We inherited little. New training ground coming. New stadium. New coaching. New youth recruitment. Good commercial team. So keep the faith."
Cisse also insisted that the Hoops can still steer clear of relegation and is taking inspiration from the club's survival last season.
"We have to keep fighting. That is all we can do," Cisse told the club's official website. "We did it last year. So why not this year again?”
The Frenchman also criticized the referee for missing a foul in the build-up to the visitors' second goal.
"I've seen the video again and again, and it was clearly a foul for their second goal,” Cisse added. "He didn't attempt to play the ball. Rob couldn't do anything. It was a clear foul and it cost us dearly. We all feel sympathy for Rob. It wasn't his fault. There was nothing he could do. He was clearly fouled. Everyone in the stadium was waiting for the referee to award a foul. He didn't, and it's cost us points."