Atletico Madrid president Enrique Cerezo promised his side will 'push on' from the third qualifying round after marking their return to the Champions League with a tie against Schalke.
Los Rojiblancos could have been drawn against the likes of Liverpool or Juventus after an 11-year absence from the competition left them unseeded in the draw on Friday.
But Cerezo still warned his club had been drawn against a 'strong side' in the Gelsenkirchen outfit.
'Every team is tough and when there's a draw you have to pit yourself against the rival that fate gives you and that's that,' he said.
'We've been drawn against a strong side, a German side, but in any case we're going to give it everything because Atletico Madrid are going to push on from this round.'
Atletico will travel to Germany for the first leg on August 12/13 with the return on August 26/27.
While home advantage in the second leg is generally seen as positive, Cerezo admitted he would have preferred to play Atletico's first Champions League game in over a decade at the Vicente Calderon.
'Personally I prefer to play at home first and away after, but everyone else thinks it's always better to play away first and so I hope this is the case for us,' he said.
'But it doesn't matter whether we play at home first or away, all we need to stress is that we'll give it our all to get through this round.'
Former England boss Steve McClaren admits it was 'fate' that his FC Twente side would be drawn against Arsenal.
McClaren took the reins at the Enschede side earlier this summer and the Eredivisie outfit will make their Champions League debut after beating Ajax in a play-off last season.
'It was strange, because as soon as I joined (Twente) I knew we had the draw coming up,' said McClaren, who was sacked as England coach last season.
'I expected one of the English teams. I think fate deals you certain cards and it has dealt us this draw.
'On one hand it's very, very tough for us but on the other it is very exciting.'
He added on Sky Sports News: 'I think of all the teams we could have had, that is the toughest - or one of the toughest.
'Obviously we looked at Arsenal, Liverpool, Juventus, Schalke and we got one of the most difficult.
'In one respect it's a tough draw for us; on the other it's now an opponent we know very well, not just myself, everyone in Holland knows the Premier League well so Arsenal will be no strangers to us.'
Barcelona have been offered a comfortable passage into the group stage after being drawn against the winner of the second-round encounter between Beitar Jerusalem and Wisla Krakow.
Barca sporting director Txiki Bergiristain believes the tie presents the Catalan giants with their 'most important games of the season'.
'We will go to Krakow to watch the game. We honestly don't mind which team we face,' he said after the draw.
'We know it's 2-1 (to Beitar) at the moment so it's open and we have to wait. We know they are the most important games of the season.
'Of course it's always important for us to be in the group stage of the competition. We want to be there and of course we are working hard to be there.'
Elsewhere, Italian giants Juventus will face either Tampere or Artmedia, Fiorentina face Czech champions Slavia Prague while 2005 European champions Liverpool play Belgian outfit Standard Liege.
French Ligue 1 outfit Marseille begin away against the winners of the second-round qualifier between Norwegian champions SK Brann and Latvian side Ventspils, Turkish champions Galatasaray meet Steaua Bucharest, and Russian outfit Spartak Moscow face Irish minnows Drogheda or Ukrainian neighbours Dynamo Kiev.
Fenerbahce, quarter-finalists last season, must see off MTK Budapest in the second qualifying round before facing Inter Baku or FK Partizan, Levski Sofia are at home to Anderlecht or BATE while Portugal's Vitoria Guimaraes entertain IFK Gothenburg or FC Basle.
Anorthosis Famagusta or Rapid Vienna will welcome Olympiacos, Ukrainian champions Shakhtar Donetsk face either NK Domzale or Dinamo Zagreb, and Aalborg of Denmark will almost certainly face Rangers or Kaunas after establishing a 5-0 lead in the first leg of their second-round qualifier against FK Modrica.
Finally, Panathinaikos and Sparta Prague are on a collision course to meet in the third qualifying round providing they dispatch Dinamo Tbilisi and Sheriff Tiraspol respectively.