Newcastle, who were already without the injured DeAndre Yedlin, could have snatched their first league win of the season late on, only for Kenedy - lucky not to be dismissed for a challenge on Harry Arter - to miss a last-gasp penalty.
Benitez concedes that it was a tough afternoon for his side, but was unwilling to discuss the performance of referee Craig Pawson.
"I don't want to talk about the referee," he told Sky Sports News. "It was a difficult game. We have problems in the right-back positions - too many things went against us.
"Kenedy was the designated penalty taker. First it was Matt Ritchie but then it was Kenedy. We knew this game on paper you can be fighting with them.
"It's a pity with 10 players - you can't complain about the workrate. We had problems at the beginning, but we still had two clear chances."
Newcastle, beaten by Tottenham Hotspur last weekend, return to action with a home match against Chelsea next Sunday.