Spurs took all three points in the North-East after Dele Alli's headed winner 18 minutes into the game capped off a lively start in which defender Jan Vertonghen had put the visitors ahead before Joselu's equaliser.
Speaking to Sky Sports News, Benitez said that his side had chances in the second half to find another equaliser and praised his players for their commitment in the tie.
"We deserved at least a draw, we were fighting until the end and had chances in the second-half. You could feel fans had the belief we could do something," the Spaniard said.
"There were a lot of positives to see the team fighting. We made some mistakes and you have to give credit to the other team. We reacted well and never gave up."
Newcastle face Cardiff City in their next top-flight game.