A win would have seen the Foxes edge into the Championship play-off places ahead of the weekend's fixtures, and it looked like Nigel Pearson's side were going to end their eight-game winless run after Jeff Schlupp had headed them back in front.
But substitute Chris Burke, back after a three-game absence with an ankle injury, kept his cool to net a last-minute penalty to snatch a point for the visitors.
Curtis Davies' own goal saw Leicester take an early lead but Nikola Zigic equalised just after the hour mark.
"We knew there would be a bit of tension around the place because Leicester and Nigel will be thinking they have to win because it (the race for the play-offs) is so tight," said Clark.
"This is a big club and there is a certain expectation level here and we knew we had to use that in our favour as part of our armoury.
"We spoke about it pre-match - making sure we use that bit of tension around the place to our benefit.
"But that aside, I felt we deserved the late goal. It would have been a travesty really if we had come away from here with nothing."