The 34-year-old captain, who has spent his entire career at Anfield and is worshipped by the fans, agreed this week to continue his illustrious career in California with the Major League Soccer champions.
Gerrard has been quoted as saying he would have stayed at Liverpool had he been offered a new contract in the close season, while Rodgers admits his departure will be a huge loss.
“No doubt Steven is still a top class player and him leaving in the summer will leave a void on the pitch and off the pitch also,” Rodgers told a news conference.
“But we will have to move forward and bring in the best players we possibly can into this wonderful club.
“History shows that great players here have moved on and it’s an opportunity for the club and other players to go and grab the mantra and make their presence here felt.”
Gerrard said at the weekend the turning point in his decision to depart came when Rodgers told him he could no longer play every game.
He did not blame the club for effectively making up his mind to leave but said he was ready to commit his future to Liverpool in the summer after they finished as Premier League runners-up.
“If a contract had been put in front of me in pre-season I would have signed it,” Gerrard was quoted as saying by the Liverpool Echo on Tuesday.
“I’d just retired from England to concentrate all my efforts on Liverpool. I didn’t want my club games to be tailored.”
Gerrard can still play a pivotal role in Liverpool’s season which offers a League Cup semi-final against Chelsea, an FA Cup run and the Europa League as well as trying to climb the Premier League table and grab a top-four spot.
They are currently eighth, seven points behind fourth-placed Southampton.
“It will be tough to qualify for the Champions League but I’m looking forward to the challenge in the second half of the season,” Rodgers said. “Seven points may seem a lot but it can be whittled away.”
Liverpool face an away trip to Sunderland on Saturday.
(Reporting by Martyn Herman; editing by Toby Davis)