The Cottagers won Sunday's fourth round tie 2-1 thanks to Reed's 85th minute strike. Before then, Jun-Ho Bae had opened scoring for Stoke, though Kevin canceled the hosts' lead with his goal in the second-half.
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Afterwards, Reed said: "Really happy, a hard fought win.
"It was about sticking to our game plan. We needed to be more clinical, and it was that final pass and final decision. We were able to come out and replicate what the manager wanted.
"Amazing feeling scoring and I don't get many, so it is extra special."