The Clarets were unable to close the four-point gap between themselves and the play-off places, despite taking the lead through a header from David Edgar.
Bolton fans voiced clear displease at seeing Marvin Sordell and on-loan Southampton winger Steve De Ridder leave the action for Craig Davies and David Ngog.
But Davies converted Lee Chung-yong's left-wing cross, his first goal since joining from Barnsley last month, before former Liverpool man Ngog showed presence of mind to turn home Jay Spearing's speculative 81st-minute drive.
"We played some good stuff, we kept the ball and I think the frustration is the fact that after we scored we didn't keep the ball," said Dyche.
"That's our strength, using the ball and keeping the ball and we've seen that many times lately.
"That was my biggest frustration with the players and I spoke to them about that afterwards, other than the obvious which is the outcome.
"At 1-0 I thought the frustration (among Bolton's fans) kicked in here and if we'd have dealt with the ball better and kept it better I think that would have only grown."