Pep Guardiola's side had their usual swagger in the first half at the Sanchez Pizjuan and looked to be cruising when substitute Bojan Krkic, who replaced the injured Pedro, put them ahead in the 30th minute.
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Guardiola said the introduction just after the break of Sevilla's Mali striker Frederic Kanoute, who sent Negredo clear in the build-up to the home side's goal and twice came close to scoring, had made the difference.
"They (Sevilla) are a very good team and have been playing at a high level for many years," the former Barca and Spain midfielder told a news conference.
"Kanoute gave them the continuity that they were missing," he added. "We got too little return for what we created in the first half."
He said he was "generally happy" with the result after his players' efforts in the Champions League on Tuesday, when they overturned a 2-1 first-leg deficit to eliminate English club Arsenal 4-3 on aggregate and reach the last eight.
Real continued their perfect home record on Saturday when Karim Benzema netted twice in a 2-0 home win over Hercules and with 10 matches remaining champions Barca have 75 points to Real's 70.
"We still have the upper hand," Barca midfielder Sergio Busquets said in a television interview.
"We controlled the match well apart from the first 15 minutes of the second half."
