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.
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.
