The North East county have been demoted after accepting a £3.8m financial aid package from the ECB.
"The ECB have to hold their hands up and look at the system they have created," said Vaughan.
Counties currently have to bid to stage international matches at their grounds.
Durham reportedly paid £923,000 to stage England's Test match against Sri Lanka in May, which ended in victory for the home side.
But they have now lost the right to stage Test cricket at the Riverside and will start next season with a 48-point deduction.
Durham finished fourth in Division One last year and their relegation means Hampshire, who were second bottom, have been reinstated.
"The decision has been coming," Vaughan, who also represented Yorkshire, told BBC Radio 5 live. "For many years, there have been a few counties who have gone through financial difficulties.
"These counties get put under so much pressure to bid for the right for a Test match and one-day games.
"In this case, Durham have found it difficult to find investment. This could be a lot worse for them. The ECB bailed them out."
Vaughan said he had "never liked" the process of counties bidding to host international matches.
"I never understood it," he said. "It was taking money out of the pot and putting counties under too much restraint and pressure to sell tickets."
In a statement, the ECB said it had helped Durham because of the "unprecedented seriousness" of their situation.
Former Durham and England fast bowler Steve Harmison said "nobody comes out of this looking very good".
He added: "I don't think the ECB have helped Durham in the last 12-18 months and there has been mismanagement from a Durham point of view."
Lancashire director of cricket Ashley Giles, England's former T20 and ODI coach, said the ECB's policy of trying to "create competition" in order to spread Test cricket throughout the country had "backfired a little bit".

One person was killed and thousands were evacuated as the fire spread fanned by strong winds.
Officials said they would bring charges against the owner of an illegal landfill site, where the fire is believed to have started.
Last year, a fire severely damaged Valparaiso, a World Heritage site.
National Forestry Corporation Director Aaron Cavieres said the fire had been "pretty well contained" and that people who had been evacuated were being allowed to return to their homes.
A red alert, the highest there is, remains in effect in case the wind should change and rekindle the fire.
More than 500 hectares were burned since the blaze started on Friday.
A 66-year-old woman died of a heart attack, thought to have been brought about by the fire.
Nineteen firefighters were injured, five of them seriously.
The fire was reportedly started at an illegal landfill, where molten metal was dumped.
The blaze comes less than a year after 15 people were killed and more than 3,000 homes were destroyed in Valparaiso by another fire.
Durham's relegation to Division Two of the County Championship is a warning to others but the England and Wales Cricket Board is also at fault, says former England captain Michael Vaughan.
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Firefighters in Chile say they have managed to control a huge forest fire around the port cities of Valparaiso and Vina del Mar.