The Warrington Wolves coach – who said Hull hooker Danny Houghton would have got his vote for man of the match - admitted: “It hurts.
“It was close and could have gone either way.
“It was a terrific game, there was drama, intensity and terrific passages of play.
“It was a game of inches and I am very proud of my boys' effort and the way they defended.
“I thought they were exceptional.
“They lapsed on a couple of kick situations, which cost us.
“Marc Sneyd's second half kicks hurt us.
“I thought we did a fantastic job on him in the first half, but his second half kicks were on the money and hurt us on a couple of occasions.”
Smith said Hull's 12-10 win was credit to Radford – and owner Adam Pearson for sticking with him.
.“Congratulations to Hull, they were tenacious and kept going and going,” he said.
“It looked like they were gone at certain stages, but we came up with one or two errors which relieved the pressure.
“They have got rid of a hoodoo of never having won at Wembley and well done to Lee.
“It's great they have stuck with a young coach who was under pressure at times last year.”