Everton have been drawn to face Dinamo Bucharest of Romania in the Uefa Cup first round after going out of the Champions League against Villarreal.
Middlesbrough play FC Xanthi of Greece, while Bolton's first European clash is against Bulgaria's Lokomotiv Plovdiv.
Scotland's representatives Hibernian play FC Dnipro of the Ukraine, while Irish side Cork face Slavia Prague.
The 40 teams who survive the first round will advance to a group stage comprising eight groups of five clubs.
Everton boss David Moyes expects the Romanians to provide a stiff test for his side.
"We would rather have got something easier but that is the way the draw goes," he said.
"We don't know an awful lot about them and it will be a tough game, they all are. We have to hope the second leg at Goodison Park will be to our advantage.
"We need to make sure we have a chance of getting into the group stage when we come back."
Middlesbrough manager Steve McClaren also believes his team do not have a straightforward task against a Xanthi side featuring former Boro midfielder Emerson.
Xanthi finished fourth in the Greek league last season and McClaren said: "It looks a tough draw, especially as we're away in the second leg.
"They finished above Egaleo, who gave us such a tough time in Greece last season but you have to face good sides if you want to do well in Europe and we'll go into it with confidence.
"Emerson was a good signing for Boro. I played against him when I was at Derby quite a few times, so I know all about him. He is a very good player and very dangerous on his day."
Bolton chairman Phil Gartside admitted his side had got the draw they didn't want.
"We looked at the list of five teams we could play and which we favoured and I think Plovdiv was bottom of the list," he added.
"But it's a great honour to be representing Bolton in a European draw for the first time and whoever it is it doesn't matter.
"We will probably take 2,000 or 3,000 fans there. I don't really know where it is or how easy it is to get there - but they are probably saying 'where the hell is Bolton!"'
Hibs chairman Rod Petrie says his club have extra pressure because they are Scotland's sole representatives in the competition.
"We have something of a responsibility not only to our fans but to Scotland to do the best we can," he said.
"It's not going to be an easy trip all the way to eastern Europe but it would not have been easy whoever we got.
"Getting into the Uefa Cup is part of the prize for a very successful season last year and if we can just get through this round then we will be into the group phase with four more guaranteed games."
Slavia Prague v Cork City
Dinamo Bucharest v EVERTON
HIBERNIAN v FC Dnipro
MIDDLESBROUGH v Xanthi
BOLTON v Lokomotiv Plovdiv
Auxerre v Levski Sofia
Aris Salonika v AS Roma
Monaco v Willem II Tilburg
Banik Ostrava v Heerenveen
Bayer Leverkusen v CSKA Sofia
Besiktas v Malmo
Brondby v FC Zurich
Red Star Belgrade v Braga
CSKA Moscow v Midtjylland
Basel v Siroki Brijeg
Litex Lovech v Racing Genk
Feyenoord v Rapid Bucharest
Teplice v Espanyol
Germinal Beerschot v Olympique Marseille
Graz AK v Racing Strasbourg
Halmstad v Sporting Lisbon
Hamburg SV v FC Copenhagen
Hertha Berlin v APOEL Nicosia
Krylya Sovietov Samara v AZ Alkmaar
Lokomotiv Moscow v Brann Bergen
Maccabi Petah Tikva v Partizan Belgrade
Metalurg Donetsk v PAOK Salonika
MyPa Myllykoski v Grasshoppers
Palermo v Anorthosis Famagusta
Racing Lens v Groclin Grodzisk
Stade Rennes v Osasuna
Sevilla v Mainz
Shakhtar Donetsk v Debrecen
Tromso v Galatasaray
Valerenga Oslo v Steaua Bucharest
VfB Stuttgart v Domzale
Viking Stavanger v Austria Vienna
Vitoria Guimaraes v Wisla Krakow
Vitoria Setubal v Sampdoria
Zenit St Petersburg v AEK Athens
(Ties to be played 15/29 September)