The Foxes are third in a tight group with two games remaining and Brendan Rodgers’ side will rue a failure to take three points on Thursday.
The hosts had been completely dominant but it was the visitors who took a surprise lead when former Chelsea winger Victor Moses headed in unmarked following a swift attack.
That sparked more urgency in the Foxes and they hit back through Daniel Amartey, who met Ayoze Perez’s flick-on with a firm header.
The experienced Moses then hauled down Ademola Lookman in the box but Vardy’s spot kick was uncharacteristically timid and goalkeeper Aleksandr Selikhov got down comfortably to parry it away.
Leicester are two points behind group leaders Napoli, who have seven points after thumping second-placed Legia Warsaw 4-1 earlier.