
Sporting scored an 85th-minute goal through Marques Bruno Pereirinha to secure a 2-1 aggregate win over Bolton.
The result ends England's last interest in the competition following the elimination Wednesday of Everton (to Fiorentina) and Tottenham Hotspur (to PSV Eindhoven).
Britain's sole representative is now Scotland's Glasgow Rangers who were under pressure for almost all of the game at Bremen but held on for a 2-1 aggregate win
Allan McGregor was outstanding in goal for Rangers, keeping out the home side with a series of saves.
Diego gave Bremen every chance with an inspired goal in the 58th minute which was full reward for their domination.
The Brazilian midfielder left Steven Whittaker and Brahim Hemdani standing by flicking the ball up from his right to his left foot just outside the area before firing the ball past McGregor into the left-hand corner of the net.
But Rangers held on thanks to a point-blank save five minutes from time from McGregor who managed to get a hand to a shot from substitute Boubacar Sanogo to deflect the ball onto the bar.
"We can't complain. We had our chances and also played well but we didn't score the goals," said Bremen coach Thomas Schaaf.
"We created so many chances against such a defensively strong side - so much the worse that we didn't take them."
Diego said: "I can't remember a game where we were so much in charge and didn't win."
Bremen's defeat leaves two German sides left in the competition, league leaders Bayern Munich, who eliminated Anderlecht, and Bayer Leverkusen, who went through against fellow Bundesliga side SV Hamburg.
Along with Rangers and Sporting Lisbon, they are joined in Friday's quarter-final and semi-final draws in Nyon, Switzerland by Fiorentina, PSV Eindhoven, Getafe and Zenit St Petersburg.
By Barry Whelan, dpa