Roy Hodgson's side fought throughout the game but were unable to break down a resolute, compact Boro defence.
Lewis Wing scored the only goal of the night and it proved enough to secure the home side's progression into the League Cup quarter-final where they will face Burton Albion.
You can watch free highlights of the match on Palace TV now as well as all the post-match reaction from manager Hodgson and debutant Sam Woods.
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