Liverpool were dealt a major blow when it was confirmed Lallana - a £23 million signing from Southampton - sustained lateral collateral ligament damage during a training session in the United States.
Lallana is expected to miss up to six weeks, putting him in doubt for Liverpool's first three games of the Premier League season against his former club, champions Manchester City and Tottenham.
But speaking ahead of Sunday's International Champions Cup fixture against Olympiacos in Chicago, Rodgers told reporters the England international would be given time to recover.
"Of course it was very disappointing - it's probably going to be four to six weeks," Rodgers said at a media conference from Soldier Field in Chicago.
"He has looked fantastic in training; it was just a very simple exercise with no pressure. The medical team are looking closely at that at the moment.
"We're hopeful that he'll come back fairly quickly but there's no rush. He's a fantastic player, we just need to get him back fit and well because it's a long season."
Lallana is not the only new player to arrive at Anfield ahead of Liverpool's return to the UEFA Champions League in 2014-15.
Lazar Markovic, Emre Can and Rickie Lambert now call the red part of Merseyside home, and Liverpool are expected to add further signings before the transfer window closes.
Loic Remy, Dejan Lovren and Divock Origi are reportedly close to sealing moves to the club but Rodgers refused to shed any light on impending arrivals.
"There has been an awful lot of work that has gone on into finding players that are suitable and are going to come in and help the club progress," said Rodgers.
"But like I've always said, I'll never comment on players until they're signed and sealed - I can talk all day about them then."
