Look back at a frustrating night for Jurgen Klopp's side with Sports Mole's minute-by-minute commentary below.
"Dortmund have a great side, they are current Bundesliga champions and have five players who start for the German national team. They have huge potential, are very creative in midfield, but I think their main strength is in attack. We will try to minimise their strengths while playing to ours.
"What I do know is that it is so important to get a good result to take into the away leg. This tie will be played over 180 minutes and the first 90 will be played at home, where we have to neutralise their game and try to impose ours. However, the outcome will most likely be decided in Dortmund."
Klopp said: "We have seen and analysed a lot of Málaga games. They've been doing really well and are an experienced team with strong defensive and offensive systems. The tie is open, it's a great opportunity, and we are happy to play Málaga.
"We've played well in this season's Champions League and we want to produce more good performances. We can't say we will be disappointed if Málaga beat us – the name of the opposition doesn't matter, because Málaga are a very good side and Manuel Pellegrini is an excellent coach. We are concentrated on this game.
"Many teams have been eliminated, and Málaga and ourselves are still involved. There will be good games in these quarter-finals but I think this will be one of the best matches in the competition. The most important game of the season is this one. We want to reach the semi-finals, so let's see what happens."