With a place in the quarter-finals up for grabs, Los Che claimed a slender advantage through Brazilian striker Jonas.
And despite Sevilla still having an excellent chance to overturn the deficit in next week's return leg, Emery insists his players achieved the goals that were set before the game.
"I am satisfied and I think it was a fair result," Emery told Marca.
"It was important to have control of the match against a team with character."
While he admitted Sevilla had created problems for his side, he feels they put in an acceptable performance in all areas of the park.
"We played a complete game, but it wasn't great," Emery added.
"We lost the ball near defence and were kind to [Jesus] Navas and [Alvaro] Negredo, who are players that demand a lot [of attention].
"Considering the level of intensity and recent form, we have done well."
Valencia are back in La Liga action on Sunday when they travel to play struggling rivals Villarreal, before they head to the Ramon Sanchez Pijuan next Wednesday looking to book their place in the Copa quarters.