Zlatan Ibrahimovic had cancelled out Capel's 59th-minute strike with a cool finish 18 minutes from time, but Barca conceded a penalty almost immediately and Negredo restored Sevilla's one-goal cushion for next week's return leg.
Pep Guardiola's side have made a lacklustre start to 2010 after drawing their first game since the winter break at home to Villarreal in La Liga on Saturday.
"Sevilla were deserved winners and have made the tie very difficult for us," Barca president Joan Laporta told Canal Plus television.
"I think it's a little early to start talking about an end of an era but everyone is entitled to his opinions," he replied when asked if Barca were struggling to live up to last year's standards.
Guardiola sent out a weakened team against Sevilla, including Argentina defender Gabriel Milito, who was making his return to action after a season and a half out with a knee ligament injury.
Barca dominated a poor first half, with Lionel Messi hitting the woodwork, and Guardiola turned to substitute Ibrahimovic to pep up the attack after the break.
But Sevilla scored first when the lively Diego Perotti burst down the left and crossed for an unmarked Capel to score at the far post.
Ibrahimovic broke the offside trap racing on to Rafael Marquez's long pass, and rounded the keeper to equalise but the scores only remained level for two minutes.
An out-of-sorts Dmytro Chygrynskiy pulled back Capel as he dribbled into the area, conceding a penalty and Negredo made no mistake from the spot.
Daniel Alves looked to have levelled again for Barca in the closing stages but the referee ruled it out for offside.
