First choice keeper Joan Garcia has been sidelined through injury for three weeks and the club are cautous over rushing him back into action.
Despite looking set to start veteran Wojciech Szczesny in their penultimate game before the international break, Flick threw Livakovic in for his first club appearance, since joining from Dinamo Zagreb in August.
Barcelona won 3-1, to preserve their 100% record so far this season and Livakovic's agent Andy Bara is confident over his squad role in the coming weeks.
"I think he can help the Barca team by playing, perhaps, between five and 10 matches this season, including in the Copa del Rey, given the number of games on this schedule."
Barca return to action at home to Getafe on October 10th, and Garcia is expected to be held back ahead of a packed run of games before November.