The recently crowned UEFA Europa League champions capped a memorable week with a 3-1 victory over lowly Elche at the Estadio Ramon Sanchez Pizjuan on Sunday.
Sevilla's win on the final day of the season was enough to clinch fifth spot, four points ahead of Villarreal and Real Sociedad.
"We had a responsibility to win and secure our fifth place spot," Emery told reporters.
"Above winning, we wanted to finish the season with a good performance.
"Now we must prepare for next season and seek sustained growth."
Sevilla's successful campaign is likely to come at a cost, with captain Ivan Rakitic one of many players expected to be targeted by some of Europe's elite clubs.
But while Emery would love to retain his star players, he is not daunted by the prospect of possible departures having lost Jesus Navas (Manchester City), Alvaro Negredo (Manchester City), Luis Alberto (Liverpool), Gary Medel (Cardiff City) and Geoffrey Kondogbia (Monaco) before the start of the season.
"Rakitic has shown a lot here, as a captain, it's brought out his best," he said.
"I have respect for any decision he makes, but of course, hopefully, he'll stay and continuing growing in Sevilla.
"Sevilla is a 'cantera' club and those that come up to the first team have to show they have what it takes to play in the Primera (Division).
"There's always a chance that many players will leave, but it’s something that, until now, I haven't given much thought.
"Losing players doesn't have to be scary, because Sevilla is always able to replace them guaranteed."
