Rodgers also confirmed that he had allowed Andy Carroll to join West Ham on loan in an attempt to secure regular football for the striker but kept tight-lipped over the futures of Charlie Adam and Jay Spearing.
The Ulsterman revealed that the Reds would be in the market to sign additional players before the transfer window shuts on Friday evening.
He told ESPN: "Andy leaving was on the understanding that he would go out and get games, as he would not get many here. He is going to West Ham to get games, and we have the opportunity to get another player tomorrow.
"There’s been lots of movement, so we’ll see what happens, and we have a number of targets.
"There’s been nothing as yet [on Spearing or Adam], as we wanted to concentrate purely on the game. Now the game is done, we will get an update on that."
A late Luis Suarez strike saved Rodgers' side from going into extra-time after David Templeton handed the visitors the lead in the 85th minute following a mistake from Pepe Reina.
Despite the nervy ending at Anfield, Rodgers says that he was never worried about his side's progression after what he described as an "excellent" performance.
"I felt reasonably comfortable throughout. Hearts worked hard, but Jose Reina’s goal was never under threat. Once the goal went in, we had to respond, and we did.
He added: "We didn’t lose, which is important. It was off the back of an exceptional performance, and the boys have been excellent, so I have no complaints there. It was important to keep the faith and keep passing. We’re delighted to be through, it’s a job well done."
Adam Morgan made his first start for the Reds in the match, and Rodgers revealed he will be looking to give more young players a chance in the team while he is in charge.
He said: "He’s a local boy, from Liverpool, and it’s important for me to give local boys who came through the ranks a chance.
"It was important for him to get his first start, and it’s important for me to give local boys a chance, and it’s something I’ll look to do."
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