Liverpool signed Balotelli for 16 million pounds ($22.81 million) following the departure of Luis Suarez to Barcelona in 2014, but the Italian endured an unsuccessful season at Anfield before returning to Italy on loan for this campaign.
Rodgers, whose tenure at the club ended in September, said he did not believe the Italian forward was suited to Liverpool's style of play, but the club's owners thought signing Balotelli could prove to be a bargain.
"When we were struggling to get in the type of player we wanted for that role, the ownership thought this (Balotelli) was a player I could maybe develop," Rodgers told Sky Sports on Sunday.
"They thought this is a 50 million pounds player that they can bring in for 16 million, and I can maybe develop him how I developed a few of the other players.
“When the owners want you to go down that route and there are no other options, you give it a go."
Balotelli scored just four goals in 28 appearances for Liverpool in a disappointing season where the Merseysiders finished sixth in the Premier League.
Rodgers said the club had targeted Sanchez and felt the Chile forward perfectly fitted the profile of player they were looking for following Suarez's departure.
He eventually signed for Arsenal, leaving Liverpool with a last-minute dash to find a striker.
“The huge blow for us was that we felt we could get Alexis Sanchez," Rodgers said.
"We thought he was the like-for-like replacement, we thought he would be perfect for us how he pressed the game, how aggressive he was in his quality.
"We felt with Luis gone, we would get Sanchez in, it would be a smooth transition into the team."
Liverpool lost to Manchester United 1-0 at home on Sunday and sit ninth in the table under new manager Juergen Klopp.
(Reporting by Toby Davis; editing by Justin Palmer)
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