Fulham, embarking on their second European campaign, can look forward to a match against a Roma side able to call upon Francesco Totti.
"We are seeing this as an adventure," said manager Roy Hodgson.
"We are aware that for a team like Fulham to even reach this stage is a fantastic achievement.
"We will do our best and put on a good performance but I will not have sleepless nights if we lose to Roma. I will have sleepless nights if we are bottom of the Premier League and that is why it has to be the priority."
In recent years Roma fixtures against Chelsea and Manchester United have been marred by violence.
But Hodgson added: "I think that the fan violence is mostly prevalent when they play their local derby against Lazio or when Juventus or Inter or Milan are the visiting teams.
"I can't imagine that at this stage of the competition a team like Fulham or a team like Basel or Sofia going to engender the type of hatred that will get their fans sharpening their knives."
Celtic face a Hamburg outfit that finished fifth in the German Bundesliga last season under Martin Jol, who has now departed for Ajax.
"It is always good to win a competition, but it would be particularly good to become the first winners of the Europa League," said Celtic's Head of Operations Ronnnie Hawthorn.
"Especially as we were also the first British club to win the European Cup in 1967."
Tony Mowbray's side must also negotiate trips to Israel and Vienna, where they will take on a Rapid side that knocked Aston Villa out of the competition.
There are 48 teams at this stage of the competition, split into 12 groups of four, with the top two qualifying for the next round.
They will be joined at that stage by the eight teams that finish third in their Champions League group.
The first round of matches is scheduled for Thursday 17 September, with the final taking place in Hamburg, on Wednesday 12 May, 2010.
Shakhtar Donetsk, who triumphed in the Uefa Cup in May, will be aiming to become the first team to win the competition in its new format.
Meanwhile, Uefa is to experiment during the group stages with having five referees per match in an attempt to combat players' diving to win penalties and to help resolve other issues.
Two extra officials will stand next to each goal, behind the dead-ball line, to spot infringements and Uefa hopes the move will mean less foul play and simulation by players.
The move is also designed to help determine whether the ball has crossed the goal-line when there is doubt.
Uefa president Michel Platini said: "One day players will give up simulating because referees will see them.
"For years players have cheated because the referees were not of a good enough quality.
"I am convinced, with the extra officials, that if you have referees close by it will prevent players from simulating and they will take the right decision.
"I have always said it is better to have more referees than a multiplication of disciplinary procedures or to refer to videos during matches."
The move comes after Arsenal's Eduardo won a penalty in Wednesday's Champions League qualifier against Celtic - even though there looked to be little contact between the striker and keeper Artur Boruc.
Ajax Anderlecht DinamoZagreb Timisoara
Valencia Lille Slavia Prague Genoa
Hamburg Celtic Hapoel Tel-Aviv Rapid Vienna
Sporting Lisbon Heerenveen Hertha Berlin Ventspils
Roma Basel Fulham CSKA Sofia
Panathinaikos Galatasaray Dinamo Bucharest Sturm Graz
Villarreal Lazio Levski Sofia Salzburg
Steaua Bucharest Fenerbahce FC Twente Sheriff
Benfica Everton AEK Athens BATE
ShakhtarDonetsk Bruges Partizan Belgrade Toulouse
PSV Eindhoven FC Copenhagen Sparta Prague CFR Cluj
Werder Bremen Austria Vienna Athletic Bilbao Nacional
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