FIFA has been in crisis since May when 14 executives were indicted as part an FBI investigation into corruption and last week 16 more officials were charged by US authorities.
FIFA president Sepp Blatter and UEFA president Michel Platini are each serving a 90-day suspension while a Swiss criminal investigation into the bids for the 2018 and 2022 FIFA World Cups in Russia and Qatar was launched earlier this year.
Beckham, who was part of the FA delegation aiming to win the 2018 bid, was asked whether the arrests and the prospect of a new president in 2016 meant FIFA was turning a corner.
"No - they are just hitting the bend," Beckham told the Christmas issue of Radio Times.
"There's a lot still to be done. It's such a mess that it's going to take a while to sort out.
"For me to see the game, the way it's been treated and looked after, is devastating. It's disgusting."
There have been repeated calls for the 2018 and 2022 elections to be re-run, with 16 of the 24 committee members serving at the time of the bids either already punished for misconduct or currently under investigation.
The Qatar tournament in 2022 has come under particular scrutiny, given the tournament will need to be played in the winter months due to the high risk to players and fans from temperatures that can reach 50 degrees Celsius in summer.
It has been proposed that the competition will instead start in November and despite the difficulties, Beckham insists 'they'll make it work'.
"Whether it's corrupt or not, those countries have been chosen," Beckham said. "People need to get behind that. It's all about bringing football to new countries. I think they should stick with it."
Beckham is also working to spread the game's global appeal and is pressing ahead with plans to create a Major League Soccer franchise in Miami.
A site for the franchise's stadium has been approved by Major League Soccer after Beckham's team of investors acquired land in Miami's Overtown neighbourhood last week.
The former Manchester United midfielder says they are 'on course' to enter the league in 2018 and is confident 'a couple of big players' can be lured to the club.
"Someone sent me a message yesterday asking if it had all fallen through. No," Beckham added.
"We're not telling everyone what's happening constantly but it's all coming good."
