Kompany, like many of his team-mates, claimed City could turn the tables on the Catalan giants after escaping from the first leg of their Champions League last-16 tie trailing by a not insurmountable 2-1 deficit.
It looked like being a far more harrowing night at the Etihad Stadium as Lionel Messi and co outplayed City in the first half, scoring twice through Luis Suarez and threatening several more.
Dani Alves hit the bar, Joe Hart denied Suarez another and Neymar had an effort cleared off the line, while Messi was almost untouchable.
But City recovered after the break, pulling one back through Sergio Aguero and - after surviving the sending-off of Gael Clichy - they can look to Hart's injury-time penalty save from Messi as a source for further momentum.
Kompany said: "It was a bad first half but definitely we were very hopeful at the start of the second half.
"That is what we should look at and say is what we need to do when we go and play them over there
Of course there is hope.
"We were due some luck and Harty is a top goalkeeper
He did what he had to do and we have hope."
Clichy was dismissed - possibly harshly - for two bookable offences in the second half, prolonging City's disappointing run of red cards against Barcelona.
City had players sent off in both legs when they met the Spanish side at the same stage last year, in a tie they lost 4-1 on aggregate.
Kompany, 28, said: "You want to play games with 11 men
It has been happening a lot for us
Really what we need to try to do is finish a game with 11 men and see how that goes."
Spanish playmaker David Silva, who set up Aguero's goal, is also hopeful the tie can be retrieved, although he did not hide from the fact City were second best for the majority of the game.
City travel to the Nou Camp for the second leg on March 18.
The 29-year-old said: "If we play like we did in the second half, we can go through, but we have to get better.
"In the first half, we weren't good - they were much better
They were much more cohesive than us on the pitch, picking up all the loose balls
Until the goal we were in it but once they scored we were bad.
"Second half, though, we got better
We had chances to equalise but once the red card came, we couldn't do more."
Defender Pablo Zabaleta, who was sent off in the 2-1 loss at the Nou Camp last March, echoed those sentiments.
The Argentina right-back said: "We were looking for a better result but if you look at the performance of the whole game, 2-1 is a good result
They weren't much better than us.
"In the first half they created a lot of chances, we were giving the ball away too cheaply but I think we improved in the second half, where we were more aggressive, more intent
We created a few chances to score goals.
"I think the performance in the second half is what we have to do from the beginning in the second game
When you are not aggressive enough against those teams it is really hard, they have fantastic players who can make a difference at any time."
Zabaleta was penalised for the late foul on Messi that led to the penalty
He acknowledged his error and thanked Hart for the save, from which Messi then headed the rebound wide to further relief.
Zabaleta, 30, said: "Players like Messi, they are so quick
Last minute of the game, inside the box, I probably should have stayed on my feet, but sometimes those mistakes happen.
"Joe Hart was there to stop it
It was a fantastic save
In those key moments he was the man
After the game I went straight to him to say thanks."
Hart also hopes the team can take full advantage of the reprieve his save afforded them.
The England goalkeeper said: "Hopefully it proves to be important, as the open goal (Messi missed) just after it
I won't decorate it - the save wasn't that good, but hopefully these little things can turn tides."
Source : PA
Source: PA