The Reds came into the Monday Night Football clash with City on the back of an unconvincing home victory over Southampton on the opening weekend, and their display at the Etihad was similarly disappointing.
The news of Balotelli's arrival will provide a welcome lift to the Merseysiders and Rodgers believes, despite his past misdemeanours, the enigmatic Italian can be a big hit at Anfield.
"All my life, I have given players an opportunity," Rodgers told Sky Sports.
"He (Balotelli) is 24 years of age, and has become a father now.
"He knows he has responsibility, not only to himself but to this great club.
"We will treat him no differently. He is part of our team.
"The market was very limited as to what we could bring in. The business was very good for us."
Liverpool will be the fifth club that Balotelli has played for and Sky Sports pundit Gary Neville says top teams will not want him if he fails to live up to his potential at Anfield.
“When he starts games, his goal ratio has been pretty good,” he told Monday Night Football.
“They are getting a goalscorer. They needed somebody else up there with Daniel Sturridge. They can’t compete on all levels and not have another presence.
“I have to say he played at City, who were the champions of England at the time, AC Milan is a great club and he played for Italy and the demands that Cesare Prandelli put on him. He has played under pressure in the last few years.
“This is his last chance at what you would call a big club and he has got to deliver.”
Fellow pundit Jamie Carragher believes Rodgers is taking a risk with Balotelli.
"Looking at the situation Liverpool were in, one week until the window shuts, they needed a striker and they're getting the Italian number one striker for £16million," he told Sky Sports.
"I think it is good business from Liverpool but there has got to be a worry signing Balotelli .
"There's a reason he costs £16million and has moved so often within his career already. That is a problem for Liverpool.
"If we could see the Balotelli we saw at Euro 2012 I'd say 'It's a great signing' but I don't want to see the Balotelli I saw at City in a Liverpool shirt: petulant, stupid, sendings-off, walking about.
"I played against him two or three times (and he was) doing nothing in the game and you knew if you got tight to him and put him under pressure he'd fall out again."
Reflecting on the Premier League loss at the Etihad, Rodgers felt the timing of City's opener was crucial, with Liverpool in the ascendancy.
"For the first 40 minutes, I thought we were the better team," Rodgers added.
"But we just switched off at the end of the half. 2-0 was then difficult for us. It killed us a little bit.
"Credit to the players, they kept going. We will get better as we go along.
"We needed to be a bit quicker in our actions, in the final third... a bit more dynamic."
The former Swansea boss also revealed the extent of the late injuries to Glen Johnson and debutant Alberto Moreno.
"Glen looks like he has pulled his thigh. We will assess that tomorrow," Rodgers added.
"Moreno has twisted his ankle on the astroturf."