Foxes striker Chris Wood was the worst culprit as he smashed a penalty against the crossbar then scuffed a gilt-edged chance wide of the target.
After losing his first two games in charge, Ince will have been the happier of the two managers and while it was a first point in four games for Nigel Pearson, the Foxes boss will be frustrated his side did not cement their spot in the play-off places.
Harry Kane proved effective on his Foxes bow and the visitors were the better side in the early exchanges but had only a couple of corners to show for their efforts.
The first chance of note fell to the hosts with Gary Taylor-Fletcher drawing a point-blank save from Kasper Schmeichel although the linesman's flag was already raised.
Kane continued to cause problems for the hosts and called Matt Gilks into action with a well-struck volley while Ben Marshall fired narrowly wide.
The Seasiders had a couple of Leicester free-kicks to defend as the first half drew to a close before Tom Ince almost gave his father's side an unlikely lead but his shot drifted wide.
Blackpool picked up where they left off after the restart with Schmeichel pushing an Ince shot round the upright before Wood squandered the chance to put Leicester in front.
The lively Kane was needlessly bundled over by Neil Eardley in the area but Wood's firmly-struck penalty crashed off the top of the crossbar.
That sparked the hosts into life and Ince was peppering Schmeichel's goal with long-range efforts before more wasted opportunities for the visitors.
Chris Morgan somehow planted a free-header wide from just three yards from a Marshall free-kick and moments later Kane's cross dropped for Wood but he fluffed his lines again.
Stephen Crainey curled a free-kick wide at the other end before Wood almost redeemed himself with a glancing header that was tipped over the bar by Gilks to earn the hosts a point.