Rodgers was talking the day after files were released which cleared fans of blame for the stadium disaster in which 96 Liverpool supporters died.
Although Rodgers has only been in charge at Anfield since June, he has pledged his full support behind the Hillsborough Justice Campaign, and talked of his increased pride in managing the club.
"Like the rest of the country, I was very happy for the families and the survivors and all the people who have supported the group over the last 23 years," he told the club's official website.
"I was obviously shocked as well by some of the findings in the report. But the most important people in all of this are the families that have suffered for such a long period of time."
Rodgers was asked if the events had made him reassess the responsibilities of the job, but insists that he was aware of the size of the task that he faced when he took over, and also paid respect to Everton fans who attended a vigil for the 96 Hillsborough victims.
He added: "No, it only increases my pride in managing the club. I was aware of the task well before I came here. I repeat this: Liverpool is an institution.
"It is a club that is worldwide and so I was fully aware of the task. What my time here and especially last night has given me is even greater pride and responsibility, drive and determination to bring social happiness to the people who have suffered for so long. That was my recollection of standing there last night and being at the vigil. It involved all sorts of emotions.
"I must pay respect to the Everton supporters who were at the vigil last night as well. This is a very unique city - there's not too many cities where the supporters are such rivals but come together.
"This is the type of city Liverpool is, it is very much one. When they are down and they are struggling, they come together no matter what team they support. I had great pride standing there watching last night."
Rodgers also spoke out against people who sing offensive chants, stating that those who do are "idiots" that smear their own club's reputation.
He continued: "In terms of the chants, I speak as a human being and I never like to hear anything like that, whatever clubs it is, that associates people and other people's tragedies and death.
"Unfortunately you have a very, very small percentage of idiots at every club that will always try and smear a club's reputation."
Rodgers also believes that the younger players at the club all understand the situation, and says that they proved it at the ceremony.
He continued: "Everyone understands the magnitude of what has happened and they are well briefed on that history. We had a minute's silence yesterday on the field and I was looking in the eyes and the faces of the ones who have just come in and they were not bemused by it - they understood why they were in silence.
"Part of being a player, manager, coach or supporter here is understanding the history."