The Foxes threw away two separate two-goal leads at Anfield on Wednesday to draw their League Cup quarter-final 3-3 with Jurgen Klopp's side, before going onto lose 5-4 on spot kicks.
Vardy, who is normally Leicester's first-choice penalty taker, opted not to take an effort on Wednesday night with Luke Thomas and Ryan Bertrand both missing, leaving Diogo Jota to score the sudden death winner to send the Reds into the last four.
Asked why Vardy didn't step up, Rodgers said: "We couldn't take him off, but he felt his hamstring with about half an hour to go. He'd usually be our number one (taker).
"We had (Kelechi) Iheanacho and (Jannik) Vestergaard who have only been back a day but we had to put them into the game.
"We had (Marc) Albrighton at right-back, (Wilfred) Ndidi at centre-back, but we kept going right to the end and that shows the spirit they had."