Williams is included in the group due to the team's past success and history, while Lotus is also a member after finishing the 2013 season in fourth place.
But Lopez hinted to Germany's Auto Motor und Sport that the two smaller teams were bullied into signing the letter.
"Williams and us were pulled over the table," he is quoted as saying.
The biggest teams, however, argue not only that the proposed $200 million cap would not help their small rivals, but that it could not even be effectively policed.
And Mercedes' Toto Wolff is quoted on Sunday: "It makes no sense to introduce rules that are not supported by the three major teams."
The big teams' counter-proposal is for cost cuts to be achieved by introducing some new technical and sporting regulations.
"We need to find meaningful limits," Wolff explained, "such as extending the parc ferme or the curfew.
"We need to discuss, for example, whether it is sensible to fly in new parts on every day during a race weekend, or 24 hour shifts before races."
The small teams, however, are sceptical, believing that the big teams are already finding ways around the existing cost-saving measures, such as limited wind tunnel use.
"When I see the downforce of the big teams, it's impossible within the allowable limits," a representative of one small team is quoted as saying.