Challenge Cup final coaches Brian Noble and Daryl Powell both admitted surprise that the Rhinos passed up a late chance to square Saturday's Cardiff showdown.
Paul tries to make headway against Adamson
The Bulls held on to win a fiercely-contested encounter at the Millennium Stadium 22-20, but Leeds could have levelled had they kicked a penalty eight minutes from the end.
But with Bradford under severe pressure at the time, Rhinos skipper Kevin Sinfield chose to run the ball in the hope of claiming a match-winning try.
However, his gamble failed as the Bulls managed to withstand everything their great rivals could throw at them in the closing moments.
Noble said: "Personally I would have kicked to get back on level terms but they were in the ascendancy towards the end and we had just defended three or four sets on our own line and then we had to defend three more.
"That was a terrific win for the character of our side. The team were on the rack towards the end but I thought that at times we played some good stuff.
"The defence there was terrific. You can talk all you like about fast, flowing rugby but you need to be able to defend your own goal-line.
"I'm really pleased for the players. They deserved this because they have had to work hard."
With both teams scoring three tries, Sinfield's decision not to attempt a goal that would have seen him match Paul Deacon's tally of five ultimately proved the difference.
But Powell refused to castigate the player who had been the hero in the semi-final win over St Helens.
The Rhinos coach said: "Kevin has been a great leader for us and he felt it was on. It was one of those times when I felt we could have put them to sleep.
"Personally I would have taken the two, Kevin didn't. They were struggling a bit at the time and Kevin did what he thought. Good leaders back themselves but it just didn't come off.
"When a team puts so much effort in as the boys did today it's very disappointing to come away with the loss.
"It was a very close game, two well-matched teams. I thought we did enough to win it but we weren't quite good enough when we had them under pressure."