Leicester - who face Atletico Madrid in the second leg of their Champions League quarter-final on Tuesday - took an early lead through Robert Huth with Jamie Vardy adding a second early in the second half at Selhurst Park.
During Monday's 3-0 defeat of Arsenal, Palace played with an intensity that gave their visitors little chance.
"It's a tight turnaround but one that we're more than capable of".
However unlike so often in recent times, his team's confidence did not suffer.
"They probably need another couple of draws or a win in their last five games".
Leicester boss Craig Shakespeare, meanwhile, struggled to hide his disappointment after his side failed to hold on to their lead.
Then, after working his way into the box, the Leicester striker cut inside and placed a left-footed shot wide of Hennessey that the keeper could only parry into the net. This game will mean a lot to the Eagles since a victory will all but secure their spot in the Premier League next season so I am expecting them to put out an awesome performance. Palace's defence failed to adequately deal with a long throw from Christian Fuchs and the towering centre-back headed home from close range to put the visitors ahead.
Andros Townsend was next to threaten for Palace after a clever throughball from Ward down the right in the closing stages of the first half, but the winger hesitated a second too long to allow Huth to close the gap and block his shot from a narrow angle. Wilfred Ndidi's air-kick gifted possession to Schlupp on the left wing and when the full-back's cross was deflected by Danny Simpson into Cabaye's path directly in front of goal, the Frenchman scored with a neat finish below Schmeichel.
The game had fired into life and the home side worked their way back onto level terms in the 70th minute when Benteke climbed above Yohan Benalouane to head home Townsend's cross.
A winning goal eluded either team, denying each a sixth league win from seven.