York City co-owner Julie-Anne Uggla has written an open letter to the EFL and National League about the "glaring imbalance" of the promotion system.
In February the 72 clubs in the National League, including those in the North and South divisions, started the 3UP campaign that called for three teams to go up from the fifth tier into the Football League.
Automatic promotion into the league did not exist prior until 1987, with the bottom four EFL clubs instead having to survive a vote of member clubs to keep their place. A second promotion place was introduced in 2003 via the play-off system.
York missed out on promotion this season after finishing second behind league winners Barnet then losing to Oldham - who they finished 23 points and three places ahead of in the final table - in the play-offs.
The Latics beat Southend in Sunday's promotion final to secure a return to League Two.
Uggla and her son Matthew took over at York City, who were relegated from the Football League in 2016, in May 2023.
"I am writing to express my deep concern and disappointment at the current promotion system between the National League and League Two, following a season where York City FC, despite finishing 28 points clear of seventh place and winning 12 more matches, were denied promotion," she said in a letter published on the club website., external
"Such a glaring imbalance not only undermines sporting merit but erodes the very foundations of fair competition.
"While I am aware of the historical basis for the two-up structure, it is no longer fit for purpose. The gap between the top National League clubs and the lower EFL clubs has narrowed, and in many cases reversed, making the case for three-up promotion beyond compelling.
"The '3UP' campaign rightly reflects the sentiment of every National League club and countless supporters."
Under the existing format, the teams who finish fourth and fifth host those who finished seventh and sixth respectively before the winners of those ties play the teams who came second and third in one-off ties.
Last month, York were beaten 3-0 by Oldham in their tie, while Forest Green, who finished third, lost on penalties to Southend, who had finished seventh.