Real Madrid coach Jose Mourinho brought two printed screen-shots of what he thought were red-card tackles committed by Atletico players to his post-match press conference following Sunday's 2-1 defeat.
Tebas responded to a pro-Real article on social media with a lengthy riposte to allegations of a "conspiracy" against the 15-time European champions.
"Here they go again, the mouthpieces and the regime's television, building the same old narrative - the permanent conspiracy," said Tebas, who has often been at odds with Real Madrid and the club's outspoken president Florentino Perez.
"This article goes further - it claims that referees harm 'The business that feeds them'.
"What exactly is it asking for? Refereeing based on revenue, viewership, or the badge? What a way to understand equality in the competition.
"Real Madrid are crucial to LaLiga. But claiming that 'LaLiga is worth nothing' without them reveals the disdain for the other clubs, their fans, and their history. The competition belongs to no one."
Madrid have made a stuttering start to the season and already sit six points behind reigning champions and early leaders Barcelona in the LaLiga table.
"Claiming that referees are directed against Real Madrid is living in another galaxy," added Tebas.
"That narrative serves as an excuse to cover up other shortcomings that are plain to see in these first matches of the season.
"It's more comfortable to point to a conspiracy than to explain what's happening on the pitch."
Madrid responded to Tebas's comments later Tuesday, calling them "intolerable".
"Our club considers it intolerable that the president of LaLiga uses his institutional position to continue discrediting and attacking Real Madrid in the manner he does in each of his public interventions," the club said in a statement.
"Given this inappropriate behavior, which has persisted over time, we believe that professional football in Spain urgently needs a leader capable of managing it and developing its full potential with the fundamental duty of neutrality."
Mourinho returned for a second spell in charge at the Santiago Bernabeu in the close-season, tasked with ending a two-year spell without a major trophy.