Wright left the club on the eve of the new season, but Vaughan has denied it was because he was interfering in team selection to ensure his son - a summer signing from Liverpool - was a regular in the starting lineup.
Home fans booed him and his son on Saturday, prompting Vaughan to consider quitting.
He said: "I'm considering my own position at the club.
"I'm just not prepared to take the blame for something I had nothing to do with.
"I don't care how we play as long as we win. Our problems aren't about Ray Mathias, it's all about the way Mark Wright walked out on his job. It's that simple, they are all his players.
"The side is a shambles, the squad is a shambles. The money we've spent is an absolute embarrassment to me.
"I'm not prepared to buy any more players after the response I've received in our last two games. I'm not prepared to put another penny into the job.
"I was very disappointed with our crowd on Saturday. It was disappointing as a parent to hear the crowd booing my son, but why were they booing him – I thought he had a decent 90 minutes.
"I'm not the manager, at the end of the day the manager walked out and I was left with no alternative to find a replacement.
"The manager's job is open to applicants and the right appointment will be made if I’m still in office."