Budge, whose club has just returned to the top flight of Scottish football had stood to fill one of the three spots available to Premiership clubs.
Kilmarnock chairman Jim Mann also put himself forward for a place, but failed in his bid as well.
The Scottish Premiership will again be represented by Duncan Fraser of Aberdeen, Eric Riley from Celtic and Dundee United’s Stephen Thompson.
And there has been no change in the Championship delegation with Raith Rovers’ Eric Drysdale and Mike Mulraney of Alloa Athletic seeing off the challenge from Hibernian’s Rod Petrie and Stewart Robertson from Rangers.
Brechin City’s Ken Ferguson will continue to voice the views of clubs in League 1 and 2, with SPFL chief executive Neil Doncaster and chairman Ralph Topping also sitting on the board.