The Whites are onto a fourth manager in 17 months after Reid's departure on Monday and Dorigo said Saturday was "the darkest hour" in their history.
Leeds are bottom of the Premiership and Dorigo, who was in the title-winning team of '92, believes relegation could signal the end.
With debts of £78m, Leeds would almost certainly go into administration should they go down and Dorigo is worried there would be no way back.
"I do fear that and anybody who doesn't is being foolish," he told The Mirror.
"Just look at the statistics. They've lost seven of their last eight league games and conceded 31 goals in 12 games.
"The chairman and various experts have all been talking about administration, so you've got to fear that could happen.
"In many ways this is Leeds' darkest hour. Their debts and the manner of that second half at Portsmouth tells you that.
"Anyone who says they don't fear for the future of this great football club is kidding themselves.
"It's sad to see the mess they're in now. Only two years ago they were top of the league and looking like champions.
"They had just been to the semi-finals of the Champions League and were signing players like Robbie Fowler. Now look at them."