QPR are rooted to the foot of the table, five points adrift of safety, and were knocked out of the FA Cup following an embarrassing 4-2 home defeat to npower League One side MK Dons on Saturday.
Fernandes, who took over in August 2011, remains determined to get the west Londoners on the right track, but says if he cannot, he will step down.
The Malaysian businessman said on his Twitter account: "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."
Fernandes took over at QPR following their promotion to the top flight and has presided over three different managers during his time at the helm.
Neil Warnock was sacked last January and replaced by Mark Hughes, who was dismissed in November with Harry Redknapp named as his successor.