The visitors were three goals up with less than 15 minutes to play at Selhurst Park thanks to finishes from Joe Allen, Daniel Sturridge and Luis Suarez.
But an unbelievable comeback from the hosts, who pulled level through Damien Delaney and a Dwight Gayle double, saw the points shared, with Rodgers predicting Manuel Pellegrini's side to wrap up the title with two home wins.
"I think that we needed to win tonight, that was the simplicity of it, to keep the pressure on Manchester City," he told Sky Sports after the game.
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"But for us, it has been an outstanding season up until now. For us to get to 81 points is a great achievement for where we're at.
"We're obviously disappointed now but we'll go again. We've got a great game at Anfield now to finish the season and keep looking to build and develop what we're doing."
Rodgers was left to rue his side's "poor" defending after they surrendered a three-goal lead whilst aiming to reduce the goal-difference deficit on City.
He said: "As you can imagine it's very quiet [in the dressing room] and for 75 minutes it was an outstanding performance.
"We got the goals and the important thing was to win the game, to at least put some pressure on Manchester City but [I'm] very disappointed we conceded the three goals.
"It was real poor defending that cost us. They showed great spirit to come back into it. Even at 3-0 in the modern game it's always a difficult score but, really, with the comfort 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."