The Merseyside outfit had agreed a £8.6m deal with the Eredivisie outfit for the Netherlands international, but issues arose surrounding a long-standing knee problem during Fer’s medical.
Everton were reported to have gone back to Steve McClaren’s Twente in a bid to renegotiate the deal, but Elstone revealed the club have now called off the transfer.
“We were very excited about the prospect of a young international Dutch player coming to Goodison, and the combination of a lot of hard work we thought we had the player,” said Elstone.
“But the transfer did not go smoothly and there were some issues and, as our fans would expect, we have to put the club first, and as our track record proves, we thought long and hard about it but it did not work out.
“We have to be very careful about how we spend our money.”
Elstone insisted Everton would still look at other possible deals to complete before Thursday’s transfer deadline.
“We are still looking and there are other options for us and I refer back to our track record, and as any club we do have other options and it will not be for the lack of trying,” he added.