The Black and Whites were 10-0 down to Warrington Wolves after an hour of last year's final but dug deep to finish strongly and earn their first win at Wembley.
Radford has warned his side they cannot afford another slow start against 19-time winners Wigan.
"Last year there were a couple of players – that I won't name – that had comfortably played 80 minutes throughout the season but 10 minutes into the game at Wembley they were on their haunches looking to come off," said the Hull head coach.
"That's what can happen in big games. You've played the game that many times in your head leading up to the game, you get on the field and you just feel you've got nothing in your legs.
"That's nervous energy and you can eat yourself up using that. Hopefully we'll be a little bit more relaxed this time around and take it in our stride a bit more."
Hull have continued to show an appetite for big games this year but have been unpredictable in Betfred Super League.
Wembley is all ready for tomorrow! ⚫️⚪️ pic.twitter.com/CRqaAVJOp0— Hull FC (@hullfcofficial) August 25, 2017
Last Friday's 46-18 home defeat by Huddersfield Giants - the fourth time Hull have conceded more than 40 points - left Radford with easier decisions this week.
"Some players played themselves out of a Wembley place and some jeopardised their selection, no doubt about that," he said.
"We haven't been as consistent as we were last year so naming the side probably wasn't as difficult as it was last time around."
Only four Hull players remain from the team beaten 16-0 by Wigan in a forgettable final at a wet Wembley in 2013.
"That was a horrible time for me personally," said Radford, who was Hull's assistant coach that day.
"It was voted the worst Challenge Cup final of all time and it's not nice to be associated with that, and in essence be responsible for that. They weren't great and we were even worse.
"There was so much to learn from that – what not to do – and that helped us last year.
"The 1985 final got voted the best of all time and that's what I want. I want to flip the result on its head but I want it to be a spectacle.
The boys gearing up for team run 🏉 pic.twitter.com/do7iLa8TrC— Hull FC (@hullfcofficial) August 25, 2017
"You've got two really good teams. Gareth Ellis and Sean O'Loughlin are two of the best players our country has ever produced and if you go through the teams, there are great battles all over the place."
Hull are aiming to become the first side in the club's history to retain the trophy and Radford believes they are on the verge of something special.
"This would really put us on the map as an elite club in this comp," he said.
"When you talk about Super League, Wigan, Saints and Leeds are the names that usually roll off the tongue.
"We get this and finish the campaign how I want to finish it, we'd be in that bracket.
"I signed in 2006 and the amount of repeats I've seen of the '05 final, it got boring in the end watching it.
"A club our size shouldn't have to wait that long to have a little bit more success. Hopefully it'll come on Saturday."