Hull were unable to mark their continental debut with victory last week, as they were held to a goalless draw by Trencin at the Stadion Pod Dubnom in the first leg of the Europa League third qualifying round tie.
The Premier League side ought to be heading into the second leg with a one-goal advantage, but midfielder Tom Huddlestone inexplicably fired over the crossbar from point-blank range after his penalty had been saved by Milos Volesak.
Hull remain strong favourites to progress at the expense of the Slovakian side ahead of the second leg, and Bruce is backing his players to raise their game after a productive week on the training ground.
"It was always going to be difficult for us over there because they are already a couple of weeks into their season and had played twice in Europe as well," the Hull boss told reporters.
"For us it was our first competitive game after winding-up our pre-season programme - and it showed. But we needed a test like that against a good side with some gifted individual players.
"No matter how many friendlies you have, it's only competitive matches that get you ready for the start of a new season.
"The game in Slovakia was tough for us, but we have really been putting the work in on the back of that and we'll be better physically on Thursday, that's for sure.
"We are looking forward to the second leg and, hopefully, we can send our fans home happy."
Robert Snodgrass and Tom Ince impressed Bruce after coming off the bench in the first leg and the close-season signings appear set to be rewarded with starts when Hull go in search of a place in the play-off round.
Bruce added: "I named the pair of them among the subs in the first game because I decided it was only fair to give the boys who got us into Europe their chance.
"They deserved it, and had earned the right to play in our European debut. It was an historic occasion for Hull, and it was the right thing for those lads to be a part of it.
"But, when I brought on Snoddy and Incey in the second half, they had a real impact and certainly did enough to suggest they deserve a start in the return leg.
"There is no question they have the ability to make a difference with their pace and guile."
Trencin, who are aiming to bring Hull's European adventure to a swift end, come into the game on the back of a 2-0 victory over Spartak Trnava on Sunday.