Charlie Austin had given the hosts the lead with his 26th goal of the season but were denied the spoils in the final minutes when half-time substitute Tomasz Cywka fired in the equaliser.
The point left Burnley eight points adrift of the play-off spots and Dyche said: "The performance was patchy.
"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.
"Most of Barnsley's play came because they were given a lease of life. 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."