Oliver Glasner's Eagles beat Rayo Vallecano 1-0 to win the club's first-ever European trophy last night (May 27).
French striker Jean-Philippe Mateta scored the winning goal in the second half.
It is the club's second major trophy in a year, following on from winning the FA Cup against Manchester City last May.
That victory was celebrated with an open-top bus parade near Selhurst Park, attended by thousands.
But the club has confirmed that there will be no repeat this time.
A spokesperson said: "Unfortunately, because of World Cup commitments some of the players are going straight to international camps.
"The club is hoping to do something later in the summer instead."
The Eagles have more than 10 players to be selected for the World Cup so far, which starts next month.
However London rivals Arsenal are holding a trophy parade in north London on Sunday to celebrate their Premier League title win.
An open letter to Palace chairman Steve Parish was posted yesterday on Croydon Council's website from executive mayor Jason Perry.
Mr Perry said the council "would be honoured to work with the club to help deliver a victory parade and civic celebration here in Croydon".
He added: "For Palace fans, this would be more than a parade. It would be a moment in history. A chance for children who have grown up watching their heroes at Selhurst Park to see them bring a European trophy home.
"A chance for long-standing supporters to celebrate a journey many could only have dreamed of.
"A chance for Croydon to come together around something joyful, positive and deeply rooted in our community."