Sevilla had yet to score a goal and only managed one point from their two outings this term but French midfielder Steven Nzonzi struck in the 12th minute to put them 1-0 ahead at Levante's stadium in Valencia.
Levante came back strongly in the second half and midfielder Victor Camarasa headed a deserved equaliser in the 58th minute.
"We are going home disappointed again," Sevilla's Spain midfielder Vitolo told Spanish television.
"In the first half we were comfortable and created chances but if you don't take them you end up paying the price," he added. "We need to learn from this and turn our focus now on the Champions League."
Sevilla qualified for the group stage of this season's edition of the continent's elite club competition by winning the Europa League and were drawn in one of the toughest-looking sections with Juventus, Manchester City and Borussia Moenchengladbach.
They begin their Group D campaign on Tuesday when they host Gladbach at the Sanchez Pizjuan stadium in Seville before a daunting trip to last season's beaten finalists Juve at the end of the month.
(Reporting by Iain Rogers, editing by Pritha Sarkar)
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