Jackett's side have now won only one of their last seven games and remain six points adrift of the top six after the defeat at Oakwell.
Rob Hulse made his debut as a second-half substitute after joining on loan from QPR but he was unable to find the net on his debut as his new side struggled to create many openings.
And Jackett was forced to admit that Barnsley were the more clinical side on the night.
He said: "We created one good chance in each half, Andy (Keogh) in the first half and John (Marquis) in the second when he was through on the keeper.
"After that we didn't create enough.
"We tried to get hold of the ball in midfield, where they had an extra man and made it pay.
"When their opportunities came they took them and it was a night for the first goal and it fell to Barnsley."