The Reds were in complete control of the Selhurst Park fixture in the 55th minute when Luis Suarez made it 3-0 after earlier goals from Joe Allen and Daniel Sturridge.
Requiring a win to place pressure on title rivals Manchester City, the Reds completely imploded, allowing the Eagles to score three times in nine minutes.
That result was certainly not ideal for Liverpool, who are now only a point ahead of City who have two games remaining, and Rodgers was critical of his players for allowing Palace back into the contest.
"As you can imagine, it's very quiet," he told Sky Sports about the mood in the camp.
"For 75 minutes it was an outstanding performance, we got the goals. The important thing was to win the game tonight and to at least put some sort of pressure on Manchester City, but very disappointed that we conceded the three goals.
"It was very poor defending that cost us. They showed great spirit to come back. The comfort that we had in the game and the quality we showed to get 3-0 up, you've got to manage the game better than that.
"It's decision-making. We look at the goals - we can do better on the first one, they play a short free-kick, and probably the free-kick they had they probably played it short because they didn't want to be counter-attacked.
"We have got to close the ball quicker on the edge of the area, it takes a deflection and it's 3-1 with 12 minutes to go and extra-time and the game is still alive. It's very disappointing.
"You just have to manage the game on the field. The goals, the second one comes from our corner. We play a square pass across the edge of the box and they break away.
"It's just decision-making, you have to make better decisions in the game, and ultimately that's what cost us."
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