The French manufacturer supply four squads including reigning world champions Red Bull, with whom they have won four successive drivers' and constructors' title doubles.
But their engine has been noticeably off the pace and unreliable since new technical rules were introduced for 2014. They have recently come under fire from the Red Bull boss, who made his frustration clear after Sebastian Vettel suffered yet another terminal engine issue in the Austrian Grand Prix.
"It’s not good for Renault, it’s not good for Red Bull," Horner said afterwards.
And he has now added that the manufacturer should have followed their rivals' lead and focussed on one team.
"When you look at the engine Ferrari has made, the customers have had to adapt their cars accordingly," said Horner.
"Mercedes likewise, whereas Renault has tried to keep all of their customers happy, which is an admirable thing to do, but it's not the best way to be competitive.
"We raised our concerns as far back as the end of 2012 with the direction the project was going. But designing and building engines is not our core competence - nor should it be - we're a chassis manufacturer," he added.
"We are pushing for next year in order to have a greater scope of development," he told Italian outlet Autosprint.
"At the moment it is not possible to change the specification of the power unit without the permission of the FIA, and the federation does not give permission for performance reasons."
"But the changes will be more long-term," White added. "At the end of the day, we're not looking for excuses, because the rules are the same for everyone and we have to respect what the others have done."
Recent rumours have suggested that Renault could be ready to end its Formula One engine programme, with Red Bull potentially purchasing their facility in Viry and building their own power units for 2016. Current Caterham team principal Cyril Abiteboul has been linked with a move to the project.