The national team suffered what was arguably the biggest embarrassment in its history on Thursday, losing 3-0 to Kazakhstan in the opening match of their Euro 2020 qualifiers.
Manager Alex McLeish has come under some intense pressure following the result, while the players have also taken their share of criticism.
White, though, believes the two biggest clubs in Scotland should carry the burden.
The TV and radio presenter said on Talksport: “Celtic and Rangers should be ashamed of themselves in terms of what they’re doing or not doing in the international scene.
“Celtic are too busy, they’re too preoccupied in trying to dominate Rangers, keeping them at arms length... Rangers trying to get back, competing with Celtic.
“Celtic and Rangers are too busy undercutting each other in terms of tickets for away fans at Old Firm games... ‘give them that, that will suit them’.
“It’s pathetic. And then they’re still trapped in sectarian bile. Rangers fans, quite recently again, the finger pointed at them for verbally abusing Steve Clarke. Once they come out the dark ages and realise they have a duty to serve Scotland, they might well progress.”