The Gunners host Liverpool on Saturday for the second of their three clashes against the Reds in the space of a week.
However, it was the manner of their victory at Bolton last weekend - where the Gunners had a man sent off and were 2-0 down but came back to win with a last-gasp deflected shot from Fabregas - that has renewed the belief within the squad.
"We knew it was an important victory, especially for the confidence of the team," said Fabregas.
"We are still in the title race and for the season that is important.
"Confidence is important for any team in the world. Even if you play well, sometimes things go against you, so we showed great character and ambition on Saturday. Let's see if that is positive for the rest of the season."
Fabregas added: "All we have to do is concentrate on winning every game and that's it.
"I know we are not the favourites any more but it is just up to us to win the six remaining league games.
"The title is no longer in our own hands because Manchester United are six points ahead but winning our last games is up to us and we have to be there behind them waiting for any opportunity."