The Dutchman has failed to impress at Goodison Park since arriving from Ajax in the summer, and Allardyce had looked to move him on this month.
The move fell through on deadline day, and Allardyce has revealed more details following the Toffees win over Leicester City.
"It was a weird situation with Klaassen. Something about a sporting contract was the difficulty," said Allardyce.
"He has a sporting contract with a sporting company and that was part of the reason it failed.
"God knows how. I can't expand on any more than that. It was one of the best moves he could have got in Europe.
"We're disappointed but he should be more disappointed than us because he's not going to be playing for Napoli who are going for the Italian league."