The Merseyside outfit fail to join Aston Villa, Chelsea and Tottenham in the quarter-finals after suffering a hammering against a rampant home side in the Portuguese capital
Carlos Mane hit a double to give the hosts the lead and the crushing scoreline was extended by Joao Palhinha's powerful effort and Wilson Janco's strike.
The Reds were suffering with a number of injuries, including summer signing Samed Yesil and American winger Marc Pelosi, who broke his leg in a match against West Brom on Monday.
It took Sporting just 11 minutes to open the scoring at the Estadio Jose Alvalade courtesy of Mane, who raced clear of the visitors' defence before showing great composure to lift the ball over onrushing goalkeeper Ryan Fulton and head into the net.
Mane doubled the advantage midway through the first half, converting unmarked at the near post, before Palhinha put the result beyond doubt in the 64th minute when he slammed into the roof of the net from a corner.
Krisztian Adorjan tested Sporting goalkeeper Mickael Meira with a long-range shot as the game meandered to a close but the hosts added a further gloss to the scoreline in the dying seconds when Janco fired home from outside of the box.
The result means that the Merseysiders fail to join fellow English clubs Aston Villa, Chelsea and Tottenham in the last eight.