Youth coach John Holt and kit-man Neil Cosgrove have lost their jobs, while it remains unclear if four on-loan players, Milan Misun, David Witteveen, Jamie Adams and Scott Findlay, can stay on.
However, the jobs of office staff at Dens Park have been secured until at least the end of the year.
Overseeing a squad that now includes just 11 permanent senior players, Barry Smith will take charge of Saturday's visit to Stirling Albion, assisted by goalkeeper Rab Douglas and coach Matt Lockwood.
This is the second time in seven years the Tayside outfit has entered administration and investor Calum Melville has paid £200,000 into the club lawyer's account to help steer the club through the process.
"I know a number of people have come forward to pledge funds, which is fantastic," said Melville.
"I'm hoping if there is anyone else out there who can help the club financially, they will come forward and do so."
Chisholm and Dodds joined the club in March, when they were persuaded to leave Queen of the South after Jocky Scott was sacked while Dundee were sitting on top of the First Division.
This is the lowest point in my career
"We're angry and people have to be made accountable," former Scotland striker Dodds told BBC Scotland.
"We don't have regrets about taking the job but questions need to be answered.
"I've been involved in a few highs and lows in football. This is the lowest point in my career.
"There is no doubt it's a grim situation and this had to be done for the club to go on. For the club to survive people have to go, it's as simple as that.
"But as long as this club survives, that's the main thing, from an overall perspective."
Dundee previously entered administration in 2003 but survived and retained their Scottish Premier League status until 2005, when they were relegated.
Defender Paton admitted that he felt let down by those running the club.
He said: "For a club to go into administration so quickly after coming out of administration, there is no hiding where the problems have lain.
"It must have been on the horizon for a wee while but they've still been signing players up to three weeks ago."
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