The duo have both suffered defeat in final of the European Cup, with Costa’s Atletico Madrid losing to cross-town rivals Real this year, and Fabregas falling to Barcelona whilst playing for Arsenal in 2006.
They have started their careers at Stamford Bridge in scintillating form, storming to the top of the Premier League table, although they have yet to prove themselves in the Champions League with the Blues, with Costa failing to score in his two European outings - although Fabregas has one goal and one assist in two games.
They return to continental action next week, and the duo are keen to add the trophy to their collections, with it being the ‘pinnacle’ of a players career.
Speaking to the Standard, Costa, who has nine goals in as many games since his arrival in West London, said: “When you get to the Champions League Final, it’s different from anything you’ve experienced.
“It’s the pinnacle of your career so it is hard to overcome that disappointment. I have to keep on working hard. I still have many years ahead of me and I hope I will play another final and have another opportunity to win this competition.”
Fabregas added similar thoughts on the competition, having also lost in semi-final ties on three separate occasions whilst with Arsenal and Barcelona.
“It is a competition I’m fond of,” the midfielder added.
“I played in the final which Arsenal lost in the last few minutes. It was incredibly sad. I have also played in many semi-finals. But in the final you can practically touch the trophy.
“I’m not going to deny that the Champions League is the competition that I still need to get my hands on. I want to win it and doing so would give me enormous satisfaction.”
The addition of Costa and Fabregas has given cause for many to suspect Chelsea will win the Champions League this season, and Costa believes that the possession of ‘two top quality teams’ will be the difference between the Blues adding their second European Cup, or ending the season without a trophy.
The Premier League leading goalscorer said: “At Chelsea we have two top quality teams, 22 players here that can make the starting line-ups of every team in the world and we have to take advantage. I think we can achieve great results this season.”