The Bulls, who are currently ninth in the Super League table, are one of the most decorated sides in English rugby league.
They have been crowned Super League champions four times, with their last victory coming in 2005, and won the Challenge Cup on five occasions.
Administration means the Rugby Football League is now likely to hand them a points deduction and this would almost certainly scupper their hopes of making the play-offs for the first time since 2008.
Guilfoyle admitted that the meeting he had held with the club's staff prior to the public announcement about going into administration had seen tempers flare.
"The position of the staff is that their wages were paid for June but there may be redundancies," he told BBC Radio Leeds.
"The meeting I held with the staff was very difficult and the longer it went on the greater the feeling of animosity there was towards the directors who were there.
"There's a general feeling of unhappiness but I hope they realise that by binding together they can demonstrate what a fantastic club this is."
Former acting chairman Stephen Coulby revealed the club was in a worse predicament when he came in in the middle of May than had been thought and this has put potential investors off.
"Within 24 hours of getting through the door we found the situation was worse than we had previously assumed," he said
"We ultimately came to a figure of £1.2m to keep the business running to next year.
"What people have been saying to us is why would they put in money now when they can't see the club benefiting to the extent they want."
It is understood Bradford currently owe £196,000 in PAYE tax for May and June, plus an outstanding VAT bill of £250,000 from the sale of the lease of Odsal to the RFL, while the monthly wage bill is over £200,000.
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