Rovers sit bottom ahead of the visit of their fierce rivals, although they are level on points with Leeds Rhinos.
Defeat at London Broncos - who had been last in the table - last Thursday leaves them in the relegation spot as they prepare to face a red-hot Hull team who are clear favourites.
The prolific Black and Whites are up to third and have lost just once in the last seven games, fully intent on, among other things, gaining revenge for a last-minute opening night defeat at KCOM Craven Park back in February.
Still,Smith - who takes charge for his first derby and only replaced Tim Sheens earlier this month - points to Rovers' shock 16-14 win over second-placed Warrington Wolves in only his second game at the helm, as an example of what can be achieved against the odds.
“That’s the beauty of our sport, isn’t it?" he said.
"Enthusiasm usually wins. Not always, but usually.
"I’d suggest that was the difference in the result a couple of weeks ago when we beat Warrington.
"I don’t think we were particularly better than Warrington but we were a little bit more enthusiastic in some areas.
"That was the great difference and a great example of it."
Smith, who is set to give a debut to new signing Matt Parcell, said: "We need to be smart and enthusiastic.
"If we do both those things it gives us a chance. But they’re a terrific side and showed what they’re able to do last week (winning 50-10 in Catalans).
"If they get somebody on the ropes they’ll put them to the sword in a big way.
"They’ve got some terrific players that play well on the front foot.
"They can be vulnerable but I think every team in Super League shows that at certain times.
"Once again it’s back to us being able to focus on our best performance and see what we can force Hull into. We’re feeling good about ourselves."
Smith says there has been a positive reaction from his squad after the 26-24 defeat at London left them in the middle of a relegation fight.
They have been competitive, only losing by a point against Wigan in Smith's first game in charge, and Wakefield Trinity, in eighth, are just four points above them.
"We don’t want to be in the position that we’re in," said the former Leeds and England boss.
"It’s uncomfortable and not pleasant. We all want to get out of that position but they (the players) have been realistic about it.
"We’ve looked at that (London) performance and taken lessons from it.
"We’re all very confident we can do something about that and improve our performances over the coming weeks.
"Ten more games? I’m telling you there will be lots of twists and turns.
"If I had to get each one of you to sit down and predict exactly how it’s going to go for the rest of the season I reckon you’d be way off. Nobody can do it. "We’re not in a great position in terms of our for and against but string a few games together and you’re not far off the top-five.
"That’s how close it is. I know a coach at another club warned his team unless they buck up their performances they could be in the mix. There’s a great chance they will be. We’re not far off."
Meanwhile, Warrington back-row Harvey Livett is looking forward to his first home game for KR after debuting at London.
The England Knights player, 22, is on loan for a month after falling down the pecking order at Wolves with Ben Currie, Jack Hughes and Ben Murdoch-Masila all fit and firing.
Livett - who played in last year's Challenge Cup final - said: "It's been really good so far.
"I've worked under Tony before - he gave me my debut at Warrington - so know what he's all about.
"It's good to work under him again and I know a few from England Knights - Chris Atkin and Robbie Mulhern - as well so it's been easy to settle in.
"I spoke to (Warrington's ex-Hull FC winger) Tommy Lineham the other day and he's experienced a few derbies.
"He told me how massive it is and how the atmospherics will be unreal down here on Thursday. I can't wait to experience it all."
Livett, who is under contract at Warrington for 2020, added: "I've been struggling to get games this year so I want to get some under my belt here and play some decent football again and then see what happens."