The Magpies suffered a seventh defeat in eight games as Wayne Rooney's strike proved the difference between the two sides at St James' Park.
"It's a bad result, but the performance of the team [was good]. It's difficult to believe that we lost 1-0," Benitez told Sky Sports News after the game.
"We had so many chances and we had so much control in the second half. They were happy with the result and they were defending, trying to play counter-attack and waste time.
"We have to manage these situations in another way after losing another game having tried so many different ways to win. We continue to make some mistakes and we've paid for that.
"After hitting the crossbar and then the post, you can see we were really unlucky, and the way we conceded the goal, even more."
Newcastle are now just a point above the Premier League's bottom three ahead of Saturday's trip to Arsenal.