City are trailing 2-0 after the first-leg of the last-16 tie and no team has managed to recover from a two-goal home defeat since the Champions League began.
However, Kompany is relishing the task and pointed out that City have form when it comes to unlikely triumphs, having scored twice in injury-time against QPR to snatch the Premier League title in 2012.
"Football is made out of nights like this," said Kompany. "If anything should give you belief, then it should be that day against QPR. We're here to try and have one of those special nights.
"It's in our own hands and that's the good thing, so I guess the message to everyone is that we have to believe.
"I'm actually very excited about this one and I think the whole team is.
"If everything goes well, we're capable of hurting Barcelona, so that's what I want to focus on.
"I like to focus on my strikers because I know that, if they score, we have a chance, but everyone needs to be at their best.
"I would say we have a chance to come here and we don't have anything to lose.
"It is all about that first goal. If we get the lead, then I believe the dynamics of the game will change.
"I am convinced of that but, obviously, it is one of the toughest places in the world to come and try to achieve something like this."
City manager Manuel Pellegrini missed the pre-match press conference as he is serving a UEFA ban for remarks he made about referee Jonas Eriksson following the first-leg defeat.
Pellegrini took a training session at the ground but is banned from having contact with the players or his coaching staff once they have arrived at the stadium for the game.
Kompany said: "It is a first for me. In 10 years I have always been used to the manager in the dressing room before the game.
"But, ultimately, it is the kind of game where you don't need too much extra motivation.
"I will presume the message will be clear for everyone before we get to the stadium, then from that moment on everyone knows what they have to do."
His assistant Ruben Cousillas was present at the press conference, and he confirmed that Matija Nastasic and Stevan Jovetic have stayed in Manchester due to injury.
Martin Demichelis is suspended after he was sent off in the first leg and England international Joleon Lescott is therefore likely to start at centre-back.