Rangers are rooted to the foot of the Premier League table, five points adrift of safety, and bowed out of the FA Cup on Saturday following a 4-2 home defeat to League One side MK Dons.
Fernandes, who took over in August 2011 following their promotion to the top flight, remains determined to get QPR back on track, but is prepared to step down if he cannot.
The Malaysian businessman, who brought in Harry Redknapp as manager in November in place of Mark Hughes, said on his Twitter account on Sunday: "Attendance was great. Thanks to fans Everything worked. We will fix It. I'm still optimistic.
"Many fans attacking me. Doing our best. As I said we won't stop trying. As I have said many times I take all responsibility and will face the music.
"Always spirit up. If can't fix it I will be first to go."