The 34-year-old was dismissed for an apparent stamp on Ander Herrera just 38 seconds after replacing Adam Lallana at half-time.
Liverpool needed a win to overtake rivals United in the race for a Champions League spot but will now be without the former England captain for the next three games.
Juan Mata put the Red Devils ahead with a neat finish in the first half before scoring a wonderful overhead kick later on to deepen Liverpool's misery. Daniel Sturridge hit one back for Liverpool in the 2-1 loss.
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The Liverpool captain now only has a maximum of five Premier League games left following the dismissal.
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