Fabianski was installed by manager Arsene Wenger as the Gunners' first-choice keeper this time last season after an injury to Manuel Almunia.
However, a similar fate befell Fabianski in January, opening the door for Wojciech Szczesny, who has since established himself as one of the best young goalkeepers in the Barclays Premier League.
But while Szczesny remains Wenger's first choice between the posts for now, Fabianski is not giving up hope of forcing himself back into Arsenal's starting eleven.
"Of course, not playing doesn't make me happy," Fabianski said on Arsenal's official website. "I want to play, that's my goal.
"But sometimes you have to be patient.
"I am just fighting, fighting [for my chance]. If there is an opportunity, I want to play as well as I can and help the team. We will see what happens."
While the 26-year-old admits it's difficult trying to force his way back into the side, especially after a long spell out injured, he is hoping to make the most of his chances, as he did on Tuesday night in the 2-1 win over Bolton in the Carling Cup.
"I am just focused on the game and of course it is hard for the keepers, especially for me as I was out for a long time, more than seven months.
"I am coming back from the injury and for the keepers the most important thing is to play regularly. Then you can build up your confidence.
"I am just trying to take every single opportunity to show that I am deserving my chance."
While Fabianski has been involved in both of Arsenal's Carling Cup fixtures this season, he insists he is ready to be called upon for league matches, although he concedes Szczesny is likely to be back in the side for Saturday's match against Chelsea.
"I don't want to be focused only on the Carling Cup and wait for that as you never know what happens during the league, and you have to be prepared for every single game.
"We are playing Chelsea [this Saturday] and obviously Wojciech will start, but I have to ready as well.
"Like I said, I have to work hard and we will see what happens.
"What else can I say about it? It is difficult but I have to accept it."
Since his debut in the 2007/08 season, Fabianski has made 58 appearances for the Gunners, racking up eighteen clean sheets in the process.