Goals from Lucas Piazon, Sone Aluko, Scott Malone and Chris Martin ensured a first win since August 27 for the Cottagers, who fell behind twice, ending a six-game drought.
Throughout that spell, Fulham have remained unbeaten on their travels, but struggled at Craven Cottage, where they have not tasted victory since the opening day against Newcastle.
They return to home soil against Norwich on Tuesday and boss Jokanovic wants some home comforts.
"After a very bad September we started after the international break with victory, that's very important for us," he said.
"It's a nice afternoon for us today, I am happy with my team.
If we want to be fighting for more important things we need to need to improve at our own stadium.
"We are a team unbeaten away, but our problem is at home. We come under pressure and we are not as comfortable without the ball as we are away from Craven Cottage.
"We showed great ambition and good character after the poor start, we showed enough desire.
"At home we have had moments where we drop after teams score. We need to improve ourselves at home. We offer good afternoons for our away fans, now we need to do it at Craven Cottage."
Barnsley went in front through Marley Watkins after just four minutes and then again after Piazon's equaliser courtesy of Sam Winnall. However, Aluko scored within 60 seconds of that goal and Malone and Martin's efforts after the break killed off the game.
It meant a fifth game without a win for Paul Heckingbottom's side, who were reduced to 10 men when Josh Scowen was sent off in the second half.
"I am disappointed, watching the goals back they were terrible on our part," the Reds boss said. "If you give four goals away like that you haven't got a chance.
"When we went in front we didn't keep the ball and weren't composed on the ball to give ourselves a rest to control the game.
"We were set up to hurt them in a way that we did with our two goals.
"Why we keep clean sheets and have defended so well was missing today."
Heckingbottom felt Scowen's dismissal, which came for a poor challenge on Scott Parker, was harsh.
"I thought he won the ball but they are saying he was out of control because he left the floor," he said. "However, he was fouled twice in the build up, why the referee wants to play advantage I don't know.
"Scowy won the ball in the box and was fouled and the referee played on. I thought that could have been managed a hell of a lot better."