Arsene Wenger's side have not lifted a trophy since the FA Cup in 2005 at the Millennium Stadium, with the team's lack of success attributed to a squad of inexperienced starlets continuing to develop under the Frenchman's tuition.
However, Fabregas - who continues to be linked with a summer move back to Barcelona as a result of the Gunners' starvation of silverware - says the time has come to knuckle down and silence the doubters.
"As a team, we need to be stronger," he said, as reported by the Press Association.
"We can't hide behind people saying we are too young or we have injuries. We just have to compete.
"People say you must learn from your mistakes, but you learn how to play football when you are 12, 13, 14, 15. You don't learn these things when you are 25.
"That is why I do not believe age is an excuse."
The 22-year-old Spaniard admitted that in previous seasons the Gunners have buckled under the pressure as the campaign has entered its final stretch.
He believes Arsenal must establish a stronger winning mentality - as possessed by rivals Manchester United and Chelsea - in order to overcome the final hurdle that stands between them and ending their five-year trophy drought
"In the past few years, we have been doing very well, but whenever it comes to important moments, maybe we haven't been up where we need to be," he said.
"We have always tried to play our football, but the goals we have conceded lately have come from defensive mistakes.
"We are a team, so we all take responsibility for it together.
"We can keep playing the same style of football, but it is the mentality that will determine whether you win trophies or not. We need an extra edge in these big games."
