Hull have slipped to defeats against title-chasing pair Chelsea and Manchester City in their opening three games, but displayed tremendous spirit to beat Norwich City 1-0, despite playing most of the game with 10 men.
Second-half goals from Alvaro Negredo and Yaya Toure consigned them to defeat at the Etihad Stadium on Saturday, but Bruce is enthused by their performances thus far.
"We’ve had three games, we’ve played 70 minutes at Norwich with 10 men, went to Chelsea and played in the second half when we got used to playing against the big boys," said Bruce.
"We need now a little bit of luck in terms of the window shutting and obviously staying injury free and suspension free. We haven't got the biggest of squads. But if we sat injury free then we’ve got a an outstanding chance.
"You bring in the likes of Tom Huddlestone and Jake Livermore and suddenly the quality of your team rises. We’re delighted we’ve got them. A lot's been said about footballers for all the wrong reasons but those have just wanted to go and play."
Winger Robbie Brady is the only Hull player to have scored this season and Bruce admitted he is still looking to bolster his attacking ranks, despite the signings of Yannick Sagbo and Danny Graham.
Sagbo is currently serving a suspension for violent conduct in his side's win over Norwich, while Sunderland loanee Graham has not found the net since January 9, when he was a Swansea City player.
He added: "It would be easy to say 'yeah, we need a striker', but the ones that are going to make the difference for us, 'will they come?' Because the ones that will make a difference will have competition and no disrespect to us as a club but that’s difficult.
"Also can we afford them? And who's out there? Who's going to get you 12 or 15 goals to make you okay?
"So it's very, very difficult but we’ll keep working away at it and see what we can do and see what we can come up with in the next 48 hours and put an end to this madness that has been this window."
Bruce did not rule out Nicklas Bendtner coming to the KC Stadium.
The 52-year-old added: "I've had him twice before and he did very, very well for me at Birmingham and Sunderland but again can we get him to come to us? And can we afford him?
"It’s difficult for us, he’s playing for Arsenal and we’ve just come out of the Championship, but we’ll see."
