The body representing Europe's leagues believes it will have greater scope to redress the growing consolidation of wealth among elite clubs in future years.
The European Leagues, which has changed its name from the European Professional Football Leagues, opposed upcoming changes to UEFA club competitions.
The top four leagues will automatically assume half of the 32 places in the Champions League group stages and the champions' route has been narrowed for smaller leagues.
Analysis presented at the European Leagues' general assembly suggests the 2018-2021 format will exacerbate the trend for the top clubs to increase their financial advantage , while new co-efficient rules favour already successful clubs.
Media Release: New UEFA financial distribution model not beneficial in improving competitive balance says European LeaguesApril 6, 2018
But with new representation on UEFA's executive committee along with seven other committees, the European Leagues feels it can ensure a fairer distribution of income.
Speaking at the meeting in Edinburgh, president Lars Christer Olsson said: "We believe that all our clubs, not just a few, should have the possibility to compete at the highest level. It is our firm view that as more and more money gets given to a small number of elite clubs, competitive balance is under threat like never before.
"It is not good for our leagues, it is not good for the vast majority of clubs and it is most certainly not good for fans."
The organisation has called for more equality between Champions League and Europa League payments as well as changes to the access list for countries when plans are drawn up for the 2021-24 cycle.
"We are very firm that some of the decisions need to be revised for the 21-24 cycle," Olsson said.
"We are convinced we will now be part of the decision-making procedure, so we will be able to influence the future of club competitions in a better way than we did before.
"We are now represented on the executive committee. And we agreed with all stakeholders, including the clubs, players, us and UEFA, that all matters which have an effect on the stakeholders should be passed by the Professional Football Strategy Council before it's presented to the executive committee for decisions. This is a major step forward.
"This means we can have a proper consultation process before decisions are made, which was not the case in the past."
LIVE | European Leagues General Assembly - Press Conference https://t.co/1H6k12PPiE— European Leagues (@EuropeanLeagues) April 6, 2018
Meanwhile, Olsson has told FIFA that proposals for an expanded 24-team Club World Cup, mooted to be held the year before every World Cup to replace the Confederations Cup, are a non-starter.
"We are totally against any Club World Cup as it has been presented so far," he said. "We are especially against the lack of consultation.
"It is not only the European Leagues, it's also the ECA (European Clubs' Association), World Leagues Forum and UEFA have made it very clear to FIFA.
"We will not accept any presentation for a new proposal, even to the FIFA council in the summer, because there is no time for proper consultation."
- Press Association & Digital Desk