Espanyol, who had lost goalkeeper Kiko Casilla to a red card five minutes before half-time, levelled the La Liga fixture at 2-2 after 76 minutes thanks to Victor Sanchez's strike.
But a fine shot on the turn by Aspas, after a pass from Carlos Bacca, saw Sevilla prevail, as Emery's men registered their sixth victory in eight league matches.
"We deserved to win and did so convincingly," Emery said at his post-match media conference.
"I'm very happy with the players' attitude in what turned out to be a very difficult game for both teams and for the ref.
"Even when we were trailing 1-0 we didn't drop our heads, we continued to press forward and looked for get back on level terms. We attacked well but our finishing wasn't as clinical as it can be."
Sevilla took 22 shots to five on Sunday with Emery's men hitting the target seven times, while Espanyol's two on-target efforts hit the back of the net.
Emery conceded the shot-conversion rate of both sides was a source of concern for Sevilla.
"Espanyol's equaliser to make it 2-2 took all of us by surprise," he said.
"It's quite normal for anxiety to start creeping in when you're drawing and time is running out but our attitude was superb.
"We do need to be more effective at the back though as Espanyol had three chances on goal and scored from two of them."
