Jermain Defoe hit a hat-trick for Sunderland with his first goal converted from an offside position.
"I'm disappointed, obviously. The big talking point is the refereeing decisions," Curtis told reporters.
"Unfortunately, the referee got all the major decisions wrong. When the referee makes a huge decision to send a player off... Kyle won the ball clearly."
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Swansea, who sacked manager Garry Monk last month, have won only one of their last 11 league games.
(Reporting by Shravanth Vijayakumar in Bengaluru)
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