Blackburn made an official approach to the Seasiders on Wednesday, before finally being given permission to talk to 37-year-old Appleton on Thursday evening.
But, Oyston was not a happy man telling the Blackpool Gazette:
And Oyston claims Pool are the victims of how their Lancashire rivals are being run at present.
He said: “Disappointment isn’t the right way of putting it.
“It’s unfortunate we’ve become embroiled in the disaster shipwreck Blackburn have become and embroiled in their antics.
“It’s a shame the way they are being run has de-stabilised us.”
And while Oyston refused to put a timescale on making an appointment talks have already been held with possible successors to Appleton.
Oyston added: “We want to get someone who we can work with and who can take us in the right direction.
“We are very conscious the transfer window is open, with less than three weeks left.
“Whoever comes in will need to trade players, both in and out.
“We need to give them the best opportunity to do that.”
Appleton was in charge at Blackpool for 64 days – just 12 games – but Oyston doesn’t think his decision to quit was a surprise.
He also dismissed reports claiming the pair had fallen out.
“Nothing comes as a surprise in football,” revealed Oyston.
“It’s not uncommon for people to come and go, although maybe not as quickly as this.
“It’s not the first time and it won’t be the last. People always default to conspiracy theories, but there was no fall out.
“We were very clear about how we do things here when we interviewed Michael.
“We make sure anyone who comes to work here is clear about how we do things.
“Any rumours that Michael and I fell out are factually incorrect.”