Ocampos collided with Blues centre-back Mason Holgate with 15 minutes left of the hour-long match, and though there seemed little intent from Holgate to bring the Argentinian down, it was enough to earn the Spanish side a spot-kick.
Everton goalkeeper Jordan Pickford got a right foot to Ocampos’ penalty, but it was not enough to prevent the only goal of a drab game.
Manager Marco Silva picked arguably the strongest side currently at his disposal, with Holgate’s inclusion the only change from Wednesday’s goalless draw at Wigan.
But throughout the game, Everton lacked cohesion and a cutting edge, with striker Dominic Calvert-Lewin particularly guilty of spurning opportunities to get on the scoresheet.
Twice in the first half the forward should have broken the deadlock, but first sliced a perfect Theo Walcott cross when heading it seemed the best option, and then fired wide having been played through by a defence-splitting Gylfi Sigurðsson pass.
Calvert-Lewin also had the best chance to equalise for Everton after they fell behind, meeting Lucas Digne’s immaculate ball, only for his header to be denied by keeper Tomáš Vaclík on 54 minutes.
Though in truth, Sevilla were probably the most deserving winners, with Everton too often sloppy in possession, especially from central defenders Holgate and Yerry Mina, who both had especially shaky games.
Silva will at least be relieved that his team came out of the friendly unscathed, though a nasty challenge from behind by Ocampos on Digne on 42 minutes put that momentarily in jeopardy, with the Frenchman needing treatment before being able to continue.
Again, though, the Blues looked like a squad desperately in need of surgery at both ends of the field, but will have the chance to make amends immediately when they face Mainz 05 in their second and final game of the round-robin tournament at 3pm BST this afternoon.
Everton team (4-2-3-1): Pickford; Digne, Holgate, Mina, Coleman; Gomes, Delph; Bernard, Sigurðsson, Walcott; Calvert-Lewin.