The Falcons announced on Friday the signing of Kiwi fly-half Gopperth on a three-year contract, which is expected to begin when the Air New Zealand Cup finishes at the end of October.
"I had my doubts about it for the past two or three days," USAP president Paul Goze told French paper L'Independant.
"With the departure of Wilkinson, the English club raised the bidding. We were no longer on the same wavelength," he added.
"There was also another problem, regarding the availability of the player.
"We really wanted him to be here for the start of our season and not at the end of the NPC (National Provincial Championship) in October.
"By the end of October, we will have almost finished the first half of next season's Top 14."
Wilkinson is set to seal his switch to Toulon once the French side are mathematically safe from the drop from the Top 14.
Perpignan, who will bid adieu to New Zealand star Dan Carter next month, will continue their search for a fly-half but Goze confirmed England number 10 Wilkinson was not on his wish-list.