Charlie Austin put the hosts ahead with his 26th goal of the season but Tomasz Cywka salvaged a point for David Flitcroft's relegation strugglers six minutes from time.
Clarets boss Dyche pointed to Saturday's exertions in beating Charlton 1-0 at the Valley as having an impact during the closing stages.
"The performance was patchy," he said. "There were parts I was pleased with and we started very brightly but the interesting thing is, we have gone 1-0 up and there is an edge and that can affect the players.
"There were a number of players who haven't played and they have gone in and put a real shift in on Saturday and they maybe looked a little tired but we felt they deserved a chance to go again because we want that competition in the group."
Additionally, Dyche bemoaned a succession of decisions that he felt hindered his side's progress.
"Most of Barnsley's play came because they were given a lease of life," he added. "Not one lease but three.
"When it is like that, the players are not stupid and they think they have a chance.
"The game should have been done. Decisions change the outlook of the game and I can't do anything about it."