An emphatic penalty from Paul Mullin cancelled out Anel Ahmedhodzic's earlier effort, but the striker missed a great chance to put the National League side ahead as Mullin's second penalty of the night was saved by Adam Davies.
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The Welsh outfit were then punished for their lack of composure as Billy Sharp put the Blades back in front in the fourth minute of stoppage-time following an error Max Cleworth.
Sander Berge made it 3-1 with a powerful finish to ensure a tie at home to Tottenham in the fifth round.
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It's heart-breaking for a Wrexham side, who were themselves moments away from victory over their Championship opponents and a glamour tie against a Premier League side when the two sides met last month.
However, co-owners Ryan Reynolds and Rob McElhenney both expressed their pride at the team.
McElhenney tweeted: "I could not be more proud of those men than I am right now. They gave it absolutely everything. [love heart emoji].
@Wrexham_AFC @espn @ESPNFC"
Meanwhile, Reynolds said: "So proud of these boys. And the 4000 plus away supporters who gave it all. @Wrexham_AFC."
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