Hospitalet threatened the Camp Nou side's defence on a number of occasions while also looking strong at the back as they managed to restrict their opponents to a solitary Andres Iniesta goal.
"They made life difficult for us with their approach. It was a very competitive game," Fabregas was quoted as saying on the club's official website.
"Our ambitions are pretty clear. What we want is to go far in all competitions. To do that we have to deliver the goods in difficult conditions, too.
"Hospitalet are a very strong and aggressive team. They closed their defensive lines well and it was difficult to create chances. However, we did manage to control the game."
Barcelona host Hospitalet on December 21 in the second leg of the Copa del Rey tie.
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