The 20-year-old Spanish midfielder reports the table-toppers in determined mood as they bid to enhance their lead over a Christmas period.
"The team is hungry and wants to achieve something to prove people wrong," Fabregas told Sky Sports News.
"We want to achieve a lot of things over the next 12 months. If we could win everything that would be perfect - but the Premier League is the competition it would be amazing to win."
Fabregas believes the departure of Thierry Henry has brought an era of opportunity for a group of players who had been playing in the shadow of the great French forward.
"I have more responsibility than before," he said.
"When you looked at Arsenal a year or two years ago you just saw Thierry Henry. It was a little bit like the other players did not exist.
"But when he left it was an opportunity for everybody to show we are a team and a good club.
"Even if the best player in the world is leaving us we can still achieve something."