The 21-year-old Leeds star was speaking after the Yorkshire side's 3-0 win at Fulham.
The Leeds fans brought another large crowd to Craven Cottage on Wednesday night as the Yorkshire side beat their west London opponents 3-0.
Goals from Byram, Mirco Antenucci and Sol Bamba - his first for the Elland Road outfit - gave Neil Redfearn's men another three points as Leeds' solid recent form continued.
And 21-year-old Byram says his side's supporters are the 'main thing' the squad is now playing for, with neither promotion (realistically) nor a battle against relegation on the club's agenda as the current season draws to a close.
"That’s the main thing we’re playing for now," Byram said of the Leeds fans. "They’re starting to turn up in even more numbers than usual.
"We’ve got a great away support and it’s about showing them what we’re building on for next season."
Leeds sit 12th in the Championship table with eight games to go, with Redfearn no doubt casting an eye over the club's plans for next season - should his future be appropriately resolved before next term, of course.
Next up for the Yorkshire team is a trip to bottom-side Blackpool, before Leeds take on Blackburn Rovers at Elland Road. After that follows a trip to Wolves and another home clash against Cardiff City.