Wanderers started a frantic final afternoon in sixth place but their promotion ambitions lay in tatters after fine goals from Matt Phillips and Ludo Sylvestre gave the rampant Seasiders a 2-0 lead with 35 minutes played.
A quickfire response stunned Ince's side in first-half stoppage time, Chris Eagles and Craig Davies the men on target for the hosts.
Despite their best efforts, Bolton could not force a winner, although a draw looked like being enough until Anthony Knockaert's late strike snatched a 3-2 win for Leicester at Nottingham Forest and denied Dougie Freedman's team a coveted top-six berth on goal difference.
Ince was impressed with how his team capitalised on an nervy start from their hosts and insisted they should have inflicted further damage.
"We should have been four or five up, to be fair, before they scored," he said. "I thought some of the football we played was fantastic.
"It was pleasing to see Matty Phillips score. I didn't think he was going to score after the first 10 minutes, he had so many chances. It was a wonderful goal.
"They looked nervous, to be honest, and how can you not be? You know how important it is to try and get into the play-off and they didn't start very well."