Goalkeeper Kasper Schmeichel appeared to have netted his first senior goal with a header from a corner, but after his effort struck the underside of the crossbar, Chris Wood forced the ball home to win the Foxes a point.
It remains unclear who will be awarded the goal, but Shakespeare has revealed that his team should feel delighted after securing a share of the spoils after a frustrating 90 minutes at the King Power Stadium.
The 50-year-old is quoted by BBC Sport as saying: "I don't really care who scored. They are both claiming it. Kasper has been looking at the video evidence. When his header came down off the bar, I didn't see the linesman signal the goal so I am pleased that Chris made sure.
"It was a frustrating game for us but I suppose, on reflection, you have to be delighted to get a late goal in the manner that we did."
Leicester are three points clear at the top of the Championship table ahead of their fixture with title rivals Burnley on Saturday.