They set up a semi-final meeting with Leeds Rhinos after beating Super League leaders Castleford Tigers 32-24 at KCOM Stadium yesterday.
The tie, to be played on the weekend of July 29/30, is expected to be staged at Doncaster’s Keepmoat Stadium and sees the past two winners of the trophy go head-to-head.
Wigan Warriors and Salford Red Devils were drawn together in the other sem-final.
Hull, who won at Wembley last year for the first time in their history, sit fourth just behind third-placed Leeds, but have a wretched recent record against their Yorkshire rivals.
“It’ll be a tough game,” admitted Radford.
“I don’t think we’ve beaten them in seven games so it’ll be a challenging match but an exciting one.
“A Yorkshire derby, too, so it’ll be exciting to be involved in.
“The was plenty of special efforts out there today and we knew that that was needed.
“We’re over the moon to be playing Leeds in the semi-final.
“This is the juicy bit of the year now; this is where the excitement starts, you’re making sure you’re spiking in those knockout games and spiking at the end of the Eights and we’ve showed a spike today.
“Castleford are top of the tree in Super League and I think Daryl Powell has done a super job there.
“But knockout football is where you’ve got to be at your best.”
Leeds Rhinos captain Danny McGuire - won won the Challenge Cup with them in 2014 and 2015 - said: “Watching Hull the past couple of weeks they have been playing well, so it’ll be a really tough game.
“We did a good job on them earlier in the season (winning 52-24 at KCOM Stadium) and when we’ve played them in the Cup recently our record has been pretty good.
“But we’ve not played them this late in the competition for a long time. “There’s a lot to play for and from the desperation they showed against Cas, it looks like they want to defend the trophy.
“It’s all on the day and who turns up and plays well.”