The Liverpool legend is under pressure after a poor season so far.
Al Ettifaq lost 3-1 to Al-Jabalain in the King Cup of Champions round of 16.
Gerrard's team have also won just three of their opening eight league games.
He said: "On the back of recent results in my position you are always aware of disappointment from fans, I have to take that responsibility on my shoulders.
"That is what I will do and continue to fight and work to improve the recent results.
"I don’t react, change or get overconcerned about social media or anyone on the outside of Ettifaq’s opinion, my priority is this club.
"I listen to the people within and continue to support my players.
"I meet Mr Hatim (head of football Hatim Al Misehal) after every game and we talk football, where it is a win, loss or draw, we have fantastic support, myself, the staff and the players from the management team.
"We did meet yesterday but we meet after every single game."