The QPR forward was expected to make an £8.5 million move to Anfield but reportedly failed a medical.
Without going into the details of why he would no longer be trying to sign 27-year-old Frenchman Remy, Rodgers said it was time to look at other targets.
"It is very simple. We have made a decision as a club not to go ahead with the deal," he told reporters after his side's 1-0 win over Olympiacos in Chicago.
"It is unfortunate for the player, it has happened before and has happened on this occasion.
"We are obviously disappointed for the player but there is nothing more to be said really and we have to move on and look at other targets."
Liverpool had reportedly agreed a fee with QPR as well as personal terms with the player.
Reports also suggested Remy was in the United States with the club's medical staff before the deal was called off.
