Chris Dagnall and Tykes debutant Jason Scotland scored the goals in the 2-0 win for the hosts at Oakwell.
The Lions, who have only won one of their last seven league games, missed the chance to move within three points of the top six.
And it was a lacklustre performance from Jackett's men, creating just a couple of decent chances in the 90 minutes.
"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," Jackett said.
"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."
Jackett said he would be speaking with Tottenham this week over the future of loanee Adam Smith.