After narrowly missing out on a Champions League berth when finishing fourth in Serie A last season, Fiorentina must now beat a side edged out by Basel for the Swiss title to claim the consolation prize of a place in the Europa League group stage.
Manager Montella lamented the outcome of the lunchtime draw held at UEFA headquarters in Nyon, which teed up an away trip for Fiorentina on August 22 and a home leg seven days later.
Montella told Fiorentina's website: "We'll be facing a team that has experience on the European stage. They've come from the Champions League qualifiers and they're into their stride having already played some important games.
"I certainly think it's one of the 'worst' draws we could have got considering the quality of the opposition. On the plus side, it's a good from a logistical perspective because, playing on a Thursday night, we would have had less time to recover if we'd had to travel further afield."
Fiorentina have never won the Europa League, nor its predecessor the UEFA Cup, although they were runners-up in the latter competition in 1990.
A pair of 1-0 defeats to French side Lyon saw Grasshoppers fail to reach the Champions League play-offs.
Sevilla have a proud recent history in Europe, having won the UEFA Cup in 2006 before successfully defending the trophy a year later.
The Spaniards will face Polish side Slask Wroclaw in the play-off round as they attempt to make another push for silverware.
Sevilla could only finish ninth in the Primera Division last term, but that proved enough to earn a place in the Europa League qualifying stages, due to Malaga and Rayo Vallecano being excluded from European competition and Copa del Rey winners Atletico Madrid earning a Champions League place.
Unai Emery's team saw off Mladost Podgorica 9-1 on aggregate in the third qualifying round and will take on a side that finished third in the Ekstraklasa last season, with Slask at home in the first leg.
Sevilla sporting director Monchi told SFC Radio: "Apart from Elfsborg this was possibly the most difficult team we could have got. It's also the shortest trip possible and we have to start studying them well because we respect them and intend to go through.
"Trips to Azerbaijan and Belarus would have been longer, but they would have been to face lower-level teams, and one thing is offset by another.
"They are a big Polish club that have been having success in recent years. They eliminated Brugge and that's something we'll have to be aware of.
"We were casually watching the game yesterday and we know they are bold and brave opponents. They were league champions in an important footballing country two years ago and we have to respect them."
Tottenham, winners of the inaugural UEFA Cup in 1972, will take on Georgian outfit Dinamo Tbilisi, while Dutch giants Feyenoord tackle Russians Kuban Krasnodar.
Feyenoord manager Ronald Koeman, whose team lost in the Champions League play-offs last season, said: "We have missed the group games in the past two years.
"For the club, the players and the supporters it would be of great value if we could get through to the main tournament."
Fiorentina's Serie A rivals Udinese will play Czech team Slovan Liberec, while another tie sees Real Betis heading to the Czech Republic first to encounter FK Jablonec, while Stuttgart will also be on their travels on August 20 when they play Croatian side HNK Rijeka.
Swansea face Petrolul Ploiesti of Romania, Eintracht Frankfurt will go up against Azerbaijani side Qarabag, while French outfit St Etienne play Denmark's Esbjerg.