The Catalan side took advantage of slack defending and scored the opener in the second half courtesy of Fabregas' well-taken finish past Diego Lopez, before Varane equalised in the 83rd minute.
The Blaugrana's goalscorer feels they could have added to their tally, but refused to be drawn into commenting on who was now favorite to secure a place in the final.
"The result could have been better for us," the former Arsenal captain told AS. "In a derby anything can happen. We are fine with the result and now we must concentrate on the league. We achieved a good result and think we will cope in the home leg."
Fabregas also commented on his side's poor start to the game, which saw Cristiano Ronaldo come close to scoring from a free kick in the opening minutes.
"As always derbies are very intense. In the first few minutes we were distant with the ball and did not compete, but after that we held on to it well."
Barcelona's assistant manager Jordi Roura, who led the team in the absence of Tito Vilanova, also bemoaned his players' lack of cutting edge, but maintained the draw was a decent result.
"We had a lot of chances to increase our lead, but a draw at the Bernabeu is always a good result," the 45-year-old told reporters. "People were saying Madrid were missing lots of players, but they have a very good squad. Those that played showed why they are at Madrid."
The second leg of the two sides' Copa del Rey semifinal is at Camp Nou on Feb. 26.
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