Sevilla hit 18 goals on the way to winning their group unbeaten, but Lazio fell into the unseeded pot after scraping through in second place with three wins and three defeats.
La Liga's other three teams in the league were also paired against tricky opponents with Valencia facing former European champions Celtic, Villarreal meeting Portugal's Sporting and Betis meeting French side Rennes.
Inter Milan, one of the teams who parachuted into the competition after finishing third in their Champions League group, will play Rapid Vienna and Napoli, also knocked out of the premiere competition, take on FC Zurich.
"We were disappointed with the Champions League exit but we are ready to have a very good campaign in the Europa League now," Inter vice-president Javier Zanetti said.
The two English Premier League sides were given fairly straightforward ties, although could face wintry conditions.
Arsenal will play Belarus champions BATE Borisov, while Chelsea visit Malmo, with both playing their away ties in the second week of February.
Elsewhere, Benfica were drawn against Galatasaray, Eintracht Frankfurt against Shakhtar Donetsk and Zenit St Petersburg against play Fenerbahce.
(Writing by Brian Homewood; Editing by Alexander Smith)
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