Jose Mourinho's side have already hit the trophy trail this season with a victory at Wembley earlier this month, and will bid to keep their treble hopes alive on Wednesday against Paris Saint-Germain in the UEFA Champions League.
With the last 16 tie poised at 1-1 going into the second leg, Fabregas is eager to ensure Chelsea put their opponents to the sword at Stamford Bridge.
"If there is one thing missing it is killing teams. Sometimes we don't kill them when we have the chance," he said.
"When we score one we have to score more and more. That’s the only way we can really improve, developing that killer instinct."
Victory over PSG would send Chelsea into the last eight of the Champions League and Fabregas is eager for his club to follow the example set by Spain during their time as the dominant side in international football.
"When you unlock the mental fear of the quarter-final, which is what we did with the national team, we felt we could become champions," he added.
"Once we were champions we were unstoppable, but you have to take this fear out and take it away. We have to believe we are the best.
"We have to be ready mentally to win every situation because this [PSG] game will not be a walk in the park."
‘Thierry Henry was my hero, but when you talk about players who have a wand of a left foot, he genuinely had that. He made my life so much easier on the right’: Ex-Arsenal star omits Gunners legend from his Perfect XI
Who is Sonia Bompastor? Everything you need to know about the Chelsea women manager
