Liverpool and Man City couldn't overcome first leg deficits against FC Braga and Dynamo Kiev - both English teams are out of the Europa League for this season.
The Reds' £35 million striker Andy Carroll couldn't score, and a goalless draw at Anfield meant Braga went through 0-1 over the two legs.
The home side's best chance came when Slovakian defender Martin Skrtel came close - but Braga's keeper Artur stood firm.
The result could mean Liverpool won't be in Europe next season - which could make it difficult to attract big signings over the summer.
Manchester City needed three goals to go through - Mario Balotelli put a great chance over the bar within the first five minutes.
But Balotelli then saw a straight red card just after the half hour following a high tackle.
City boss Roberto Mancini has said he's "very disappointed" in the striker - and that Balotelli won't be playing in their clash with Chelsea on Sunday.
Aleksander Kolarov's strike through a crowded penalty area was the only goal City could muster on the night - and they lost 1-2 on aggregate.
City's only realistic hope of silverware this season now seems to be the FA Cup - they're playing their biggest rivals Manchester United in the semi-finals on April 16.
In Scotland, Rangers needed goals after earning a 0-0 draw against PSV Eindhoven in the first leg.
Rangers needed goals after earning a 0-0 draw in the first leg; but the only goal of the match came from PSV's Jeremain Lens after just 13 minutes.
Maurice Edu's second-half shot appeared to be cleared off the line by Atiba Hutchison's hand - but the referee didn't think it was hand-ball and Rangers' European dream was over for another year.