The Toffees encountered a number of perhaps unseen problems over the two legs against their central European counterparts, and they will almost certainly not be given an easy ride in the final round before the gruelling group stages. Free-spending AC Milan are also vying to progress into the bread and butter of the competition, while last season's finalists Ajax will be trying to go one better this season after Ligue 1 outfit Nice ended their Champions League hopes earlier this week.
When is the draw?
The draw for the Europa League play-off round starts at 12pm BST on Friday 4 August from UEFA's headquarters in Nyon, Switzerland.
The clubs in contention will be judged upon based on their UEFA coefficient standing and placed into either a seeded or unseeded pot. A total of 44 teams will be drawn in total, including those that were knocked out of the third qualifying round of the Champions League. Of the 44 sides, 22 will be seeded.
The seeded teams will not have to worry about being pitted against each other. One team will be drawn from both the seeded and unseeded categories before being placed in a bowl and mixed around in order to decide who hosts the first leg. The 22 teams who emerge victorious over the two legs will join the 26 clubs who secured direct passage to the group stage.
Seeded teams - Zenit St Petersburg, Dynamo Kyiv, Ajax, Athletic Club, Fenerbahçe, AC Milan, Viktoria Plzeň, RB Salzburg, Club Brugge, PAOK, Ludogorets Razgrad, Krasnodar, BATE Borisov, Everton, Legia Warszawa, Marseille, Dinamo Zagreb.
Unseeded teams - Maccabi Tel-Aviv, Austria Wien, Midtjylland, Partizan, Panathinaikos, Marítimo, Rosenborg, Hajduk Split, Sheriff Tiraspol, Apollon Limassol, Oleksandriya, Videoton, Crvena zvezda, Skënderbeu, Utrecht, AEK Athens, Altach, AEK Larnaca, FH Hafnarfjördur, Vitorul, Osijek, Vardar, Domžale, Östersund, Shkëndija, Sūduva
When are the ties played?
The first legs are scheduled to take place on 17 August, with the returning games a week later on 24 August. The draw for the group stage will take place on Friday 25 August.
Who could Everton draw?
Ronald Koeman's side will be seeded for the play-off and as a result will not have to face the likes of AC Milan, Athletic Bilbao and Zenit St Petersburg, who are set to be the top seeds. However, a number of potential banana skins and tricky trips could still lie in wait for Everton, who could face any of the 22 unseeded teams.
Best case - Ostersund. Formed just 21 years ago, the Swedish minnows do not boast major European pedigree and have only one season of top-flight experience under their belt.
Managed by former Stoke City and Southampton full-back Graham Potter, Ostersund overcame Luxembourg's Fola Esch 3-1 on aggregate in order to make it to the play-off round but were the talk of the tournament last month when they dispatched Turkish giants Galatasaray in the second qualifying round.
The win over a Galatasaray in transition will live long in Ostersund folklore, but Everton would surely have little trouble getting past such timorous opponents and would presumably be able to leave some of their star players at home in order to focus Premier League matters.
Worst case - Maccabi Tel Aviv. Last season's runners-up in the Ligat HaAl may not be the force they once were but have very much enjoyed their recent run in Europe, winning all six of their qualifying matches in the Europa League, scoring 11 times and conceding just once.
Managed by former Barcelona and Manchester United midfielder Jordi Cruyff, Tel Aviv sit top of the unseeded teams due to their coefficient and are able to boast threats such as Omer Atzili and Vidar Orn Kjartansson, both of whom have been in sparkling form during the embryonic stages of their Europa League campaign.
Add in the factors of playing in the Netanya Stadium, which can generate a rather intimidating atmosphere, and the flying around 18 hours to get to and from Tel Aviv, Ronald Koeman's men will surely be hoping to steer clear of a trip to Israel later this month.