Bolton fell 2-0 behind inside 35 minutes, only to score twice in the seconds before half-time, but Leicester snatched a last-gasp 3-2 win over Nottingham Forest and denied them a top-six place on goal difference.
"I feel sorry for Dougie, I think he's done an amazing job since he came here and I know he's probably hurting now," Ince said.
"He's a fantastic manager, a lovely guy and he'll bounce back. It'll be the worst night in the world tonight but you have to get over it and come back stronger. I'm sure Dougie will and I'm sure the players will.
"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."
Ince was delighted with his side's play until Chris Eagles and Craig Davies levelled the scores before the break and felt they could have been out of sight had they taken a multitude of early chances.
"We should have been four or five up, to be fair, before they scored," he added. "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."