City will fight it out with the Spanish giants for a place in the Champions League final after a tense first leg at the Etihad Stadium.
Goalkeeper Hart was one of City's star players, producing two stunning late saves to preserve their clean sheet and keep them in contention.
The England number one said: "It's a 0-0 and it's put us in a good place - we believe we can go over there and get the result we need.
"It's a solid start to set up the second leg. We have had a little sparring session but next Wednesday will be a ding-dong."
Hart was modest about his own performance but, after a largely quiet night, his reflex stops to keep out efforts from Casemiro and Pepe again underlined his importance to City.
The 29-year-old has been consistently excellent throughout City's run to the last four.
He said: "I did my job, and we are still in it.
"We are playing against good teams, so I get a lot more to do. In the Premier League people don't necessarily come here to win, as a good result against us is a draw.
"But in the Champions League there is no place to hide, it's all about winning and we play against some real quality.
"It's important that I did my job and we didn't concede, but it has gone now."
City's charge to the last four of the Champions League for the first time has revitalised their campaign after a disappointing challenge in the Barclays Premier League.
It is a landmark achievement in the club's development but insists the attitude among the players is one of hunger to go even further and has thanked fans for their raucous support.
He said: "It's a good achievement to get this far, not a great one. We want more and will show that next Wednesday and on Sunday at Southampton.
"The pyrotechnics and everything looked spot on, really suited a Champions League semi-final. This is where we belong and we want to keep doing these kind of achievements."
Source: PA