The Anfield outfit booked their Valentine's date in south London with a fantastic late turnaround against Bolton on Wednesday night.
Eidur Gudjohnsen had edged the Championship outfit in front from the penalty spot with just under an hour played in the Fourth Round replay at Macron Stadium.
Bolton Wanderers 1-2 Liverpool
The FA Cup
Fourth Round Proper replay
Wednesday 4 February
Macron Stadium, Bolton
Winning club receives £90,000 from FA Prize Fund
Neil Danns then saw red for the home side after a second booking, and Neil Lennon's team were left hanging on to their slender advantage.
But Liverpool pressure finally paid off when Raheem Sterling levelled with five minutes remaining and Philippe Coutinho sealed victory with a stoppage-time stunner, and Rodgers admits the win was never in doubt.
"Even at 1-0, I expected us to win," he said. "The confidence of the team at the moment is very high.
"We had some chances in the first half and didn't quite take them. But our composure and quality after [the penalty] was very good.
"We scored two but could have had many more. But give credit to Bolton as well over the two games. Neil [Lennon] has done a brilliant job with his squad - they are very resilient and very hard to beat.
"They took us right to the very end, but it was a great win for us."
It means a return to Selhurst Park for Liverpool after suffering defeat there back in November and letting a three-goal lead slip on the same ground when challenging for last season’s Premier League title. But Rodgers believes his side has turned a corner.
And, although he is wary of their upturn in form since the appointment of Alan Pardew, the Reds gaffer is eyeing a place in the last eight of The FA Cup.
“It’s a great thing to be drawn against Palace,” he said. “We didn’t play anywhere near the expected level last time, but that was the lowest moment of the season in terms of performance.
“We go there with a totally different frame of mind and a different level of performance.
“Alan’s lifted the club since he’s been there but we’ll go there with big confidence and look to keep performing at the level that we’re at now.”
Rodgers was also delighted to see England striker Daniel Sturridge continue his recovery from injury in the 2-1 replay win over Wanderers.
And with the weekend’s Merseyside derby next up, Sturridge was made to settle for a place on the bench, but joined the action in the second half with his side a goal down.
While he appreciates that Sturridge’s return can only aid their performances, Rodgers continues to manage expectations about his return.
“It’s just about managing that game-time,” he explained. “He’s a top talent and obviously when he’s fully fit he plays, it’s as simple as that.
“Unfortunately he’s not at that stage yet. He’s a great player for us to bring off the bench at the moment and he’s getting there every day.”