Cadiz had done well in the first leg to hold Los Che to a 0-0 draw at home, but Emery's men were too strong for their lower-division opposition on Thursday, cruising to a comfortable win thanks to goals from Victor Ruiz, Jonas, Roberto Soldado and Ever Banega.
And speaking after the game, the Valencia coach was satisfied with his team's progress, admitting they had made life difficult for themselves by failing to get a result in the first leg.
"Surprises [in the competition] happen every year," Emery said, according to Marca.
"We did not want trouble, so we were mindful to go out strong and tight, to get a result which we complicated."
When asked why Valencia's display at the Mestalla on Thursday was so different from the first leg, Emery insisted the pitch at Cadiz "was smaller, they [Cadiz] were very motivated and we had no success at the rival goal".
Now looking forward to 2012, Emery has called for "continuity and growth" at the club.
"It's very good news that the new stadium is done," Emery added.
"I think we should keep growing, which means not wasting a place in the Champions League and getting closer to a title."
Valencia end 2011 third in La Liga, seven points behind league leaders Real Madrid, and have a Europa League round-of-32 tie against Stoke to look forward to.