Shaqiri sealed victory for Liverpool over their old adversaries on Sunday with two goals following his 69th minute introduction.
Both clubs have a rich tradition in the competition, each winning it five times.
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Defeat, though, leaves United sixth on 26, 11 points away from the fourth Champions League qualification slot with manager Jose Mourinho, who had left France midfielder Paul Pogba on the bench, accepting that was the best his side could now hope for.
United said they wanted fans going to the game at Anfield "to support the team in a passionate and positive way".
It was the third time this season that a mistake by Alisson has led to Liverpool conceding a league goal and no Premier League keeper has committed more errors that have directly led to goals. I felt my knee and it pops, so you just work hard and try to be back as soon as possible. "For the players, it's most hard".
"I don't think his style of play is suited for the Premier League, and we will see his brilliance in the Italian or Spanish league".
"We're obviously not playing well at the moment", former United player Denis Irwin said at UEFA headquarters in Nyon, Switzerland, after the draw.
"We can still finish fourth", Mourinho added.
They are fast, they are intense, they are aggressive, they are physical, they are objective.
Highlights from Liverpool's 3-1 win over Manchester United in the Premier League.
Elsewhere Crystal Palace showed they can win without Wilfred Zaha in their side as they beat Leicester City 1-0 although they had failed to do so in 14 games without him.
The latter and more recent clash was particularly stark, with United coming second best to the Reds in practically every statistical measure, and their play was insipid throughout. The Brazil global started and finished a move in the second minute that saw Victor Lindelof scrambling to deflect a shot behind. Never has the Belgium had so few touches of the ball during a game in which he's played 90 minutes. Young cleared Dejan Lovren's effort off the line and Firmino shot over - the ninth attempt inside 20 minutes - before the breakthrough was made.