The Argentine World Cup winner was unable to positively influence the showpiece event at Wembley in his side's favor.
Fernandez was mocked by an opposing fan as he went up to get his runner's up medal.
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"Enzo, unlucky lad," one Liverpool supporter said to the Argentine, as shown on social media fan footage from the game.
Enzo was upset and turned towards the fan, but then thought better of engaging.
Chelsea were beaten 1-0 on the night through an extra-time Virgil Van Dijk header.