Having sparked talk of interest from Spain, the Brazilian forward committed to a new contact at Anfield in April.
Those terms helped to keep him out of the gossip columns over the summer, with the likes of Barca forced to look elsewhere for attacking reinforcements.
That looks set to remain the case in upcoming windows, with Firmino – who netted 27 times for Liverpool across all competitions in 2017-18 – feeling settled in his current surroundings.
He told The Mirror: “Everyone hears stories about what it means to be a Liverpool player, but, until you live it personally, you cannot really understand it.
“In my whole life, I never thought that I would get treated like I do here.
“It’s a huge responsibility and we can only give everything back to the supporters that we can.
“The Premier League is our main challenge, but also Europe, after reaching the final against Real Madrid and falling down last season.
“That left us with a bad taste in our mouths, but we have to be patient and go game by game to achieve what we really want this time.”
Firmino’s focus for now remains locked on the present, with the 26-year-old determined to help deliver success at Liverpool before thinking about what his future could bring.
He added: “When people ask what my ambitions are for the rest of my career, I always say that I live in the present.
“I don’t look at more than what we have in front of us in the next few days.
“I’m only interested in Liverpool and winning everything I can with them. We have the best supporters in the world here, they are amazing – and there are Liverpool fans in every part of the planet.
“So we know what it would mean to be champions.”
Liverpool opened their 2018-19 Premier League campaign with a resounding 4-0 victory over West Ham, with their next outing set to take them to Crystal Palace on Monday.