Middlesbrough boss Gordon Strachan accepted his side failed to cope with Barnsley's second-half revival.
Justin Hoyte gave Boro a half-time lead but goals from Steve Foster and Hugo Colace earned the Tykes the points.
Strachan said: "We won the football match in the first half and they decided to turn it into a cup tie and then they won it. We were disappointed to lose the game but we couldn't match them in a different game."
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