City strolled to the Premier League title last campaign, registering 100 points and scoring 106 goals in the process.
Liverpool in contrast could only finish fourth, 25 points adrift of Pep Guardiola’s side, though they did beat City on route to the Champions League final.
Jurgen Klopp responded by spending more than £161 million ($211m) on new players over the summer in an attempt to close the gap.
The early signs suggest Klopp’s investment has worked, with Liverpool making an impressive start in the Premier League.
The Reds are currently third, level on points with second placed Chelsea and just two points behind leaders Manchester City, with all three sides still unbeaten.
As a result Firmino believes the Merseysiders are well placed to push City all the way as they seek a first league title since 1990.
“We have the team and squad to fight for the titles of both competitions,” Firmino told Goal. “Last season it was like that, when we reached the Champions League final and also did very well in the Premier League, although City managed to open a good lead and did not give anyone a chance to catch up.
"But the club knew where to strengthen and brought important players, including them Alisson, Fabinho and [Xherdan] Shaqiri. We have everything we need to have another great season.”
Despite Liverpool’s improving form Firmino has struggled for goals, scoring just once in his last 10 matches. Mohamed Salah has also been unable to reach the highs he achieved last campaign, where he netted 44 times in all competitions.
However, the Brazilian isn’t too concerned about the form of individuals, as long as the team are still picking up results.
"The season is just beginning. Still, the team has maintained a good level of performance,” he added. “The fact is that our attack really made a lot of goals and stood out last season and it is normal that the level of expectation increases.
“Everyone looks at Liverpool in a different way, always expecting great games and many goals. We have experienced players who know how to deal with any type of criticism.”
Firmino also praised manager Klopp for helping to develop his game.
The forward moved to Anfield from Hoffenheim in the summer of 2015 during Brendan Rodgers' reign but has emerged as one of the Merseysiders' most important players under Klopp.
"I have evolved a lot as a player working with Klopp, who is a very tactical coach,” he said,
“He’s close to everyone, which makes the environment fun. He’s managed to build a team that is not just strong in attack.
“It’s helped the team develop and return to being one of the title contenders here in England and one of the main players in Europe.”