Goalkeeper Aleksandr Selikhov saved his tame effort with second-half substitute Vardy having only been on the pitch five minutes.
Leicester go to Leeds in the Premier League on Sunday and, with Vardy having scored seven times in 14 games this term, Rodgers expects him to hit back at Elland Road.
He said: “That will be the message, he has saved this club so many times and we bring him into the game because he is a fantastic goalscorer. It was unfortunate, he was maybe a little bit cold in the game. It wasn’t to be.
“It would have been easy for him to give the penalty to Youri (Tielemans) because he’s not quite warmed up but he backs himself in the games. He is a brilliant goalscorer and if Jamie Vardy is on the pitch and there’s a penalty you wouldn’t want anyone else to take it.
“It’s one of those things, the keeper has gone the right way and makes the save but we had other opportunities in the game. We can’t just rely on that. We can do better and that’s something we can analyse and take it into the next game.”
Thursday’s draw left Leicester’s European hopes on a knife edge with two games left.
They are third in Group C, two points behind leaders Napoli with just three points separating the four teams.
Defender Jonny Evans said: “We didn’t take our chances. They made it very difficult for us, we expected that before the game and we were putting the pressure on towards the end. We got the penalty and Kelechi (Iheanacho) had a chance.
“They are the kind of chances you have to take. When games are tight sometimes you need a bit of fortune to come your way.
“We expected them to sit deep and it was going to be difficult to break them down. It can be difficult to keep your patience. We had the penalty and if it goes in we win the game. We kept pushing to the end but we couldn’t get the goal.
“It’s in our hands and at home, I know we have had two draws, but we always feel confident.”
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