
The Premiership club face an uncomfortable tie against French club Toulouse, while Celtic have to overcome Spartak Moscow to advance to the lucrative group phase of the competition.
Liverpool spokesman Bryce Morrison said after the draw: "It will not be easy. This qualifying round of the competition seems to be getting harder each year.
"The French league is strong and we know very little about them. They are a rugby town and it is a new ground for us. They will be really up for it.
"Rafael Benitez has brought in some new players and everyone in the club feels we are stronger and there is no reason why we can't go all the way again."
Friday's draw in Nyon saw fellow Premiership club Arsenal being pitted against Sparta Prague, while Lazio Rome will face Dinamo Bucharest.
Arsenal's David Miles was satisfied with the draw. "We have played them four times in six years and so we're very much looking to visiting Prague again.
"It could have been worse and we have a good working relationship with them.
"But we won't take anything for granted. It is very important for the club both financially and for our supporters to play in the group stages."
German club Werder Bremen were drawn against the winner of the second qualifying round tie between Dinamo Zagreb and NK Domzale.
Bremen's coach Thomas Schaaf said that he accepted that his club would start the tie as favourites. "We expect ourselves that we will advance to the group phase. It does not matter whom we face, we will respect both clubs and need to be at our best to go through."
Rangers, who finished runners up to Celtic in the Scottish league, need to overcome Zeta Golubovci in their second qualifying round first, and will the face the winner of Red Star Belgrade and Levadia Tallinn in the third round.
The UEFA Cup holders Sevilla were drawn against AEK Athens, while another mouth-watering tie sees Turkish champions Fenerbahce take on Anderlecht.
Former champions Ajax will face the winners of the tie between Slavia Prague and MSK Zilina, while Steaua Bucharest, who won the competition in 1986, should advance against Hafnarfjordur or Bate Borisov.
The other games see Tampere United or Levski Sofia play against the winners of Astana and Rosenborg Trondheim, while FK Ventspils or Red Bull Salzburg were drawn against Pjunik Yerevan or Shakhtar Donetsk.
Spanish club Valencia will face the winners of VSC Debrecen and Elfsborg Boras, while Dynamo Kiev face RC Genk or FK Sarajevo.
The final matches are between Benfica Lisbon and the winner between FC Copenhagen and Beitar Jerusalem and FC Zurich against Besiktas Istanbul or Sheriff Tiraspol.
The first leg games will be played on August 14 and 15, with the return legs two weeks later. The winners of the ties will qualify for the lucrative group phase of the competition.
DPA