Yorkston is frustrated that the SPL has not told his club its reasons for inviting the First Division runner-up to replace
But he will not seek to reverse the decision or take any action that holds up the league season, with the SPL due to kick off on 4
"We are now resigned to playing in the SFL," Yorkston told STV.
"Any challenge that we do would be against the decision for us not to play in the SPL now.
"We're not going to be the club that holds everybody up by appealing and delaying the start of the leagues."
SPL chief executive
Yorkston said: "We contacted the SPL to ask what the sporting merit was that they decided upon to put Dundee into the Premier League. We're still waiting on a response.
"I find it very strange. Probably, they don't have an answer to give us.
"We were originally told we would be told in two weeks which is once the competitive games have started.
"You're now telling us we're not going to get an answer. Obviously it makes it very difficult when we're working out what we're going to do.
"[They may feel] that if you don't know the reason you can't appeal against that reason. But we have to speak to our legal folk and see what they make of this latest development.
"We've been kept out of the SPL and we haven't been told why."
Tommy Oar is aiming to parlay a breakout season for FC Utrecht into a telling contribution for his country as Australia faces its FIFA 2014 World Cup destiny next month.