Cousins, the Denver Nuggets' backup center, exited Game 1 with 10:28 left after being whistled for two consecutive technical fouls.
Cousins appeared surprised after he was whistled for the first technical and seemed to be arguing with an official when he drew his second and an automatic ejection.
Nuggets coach Michael Malone said he didn't think Cousins did anything to warrant the technical fouls.
"It happened right in front of me," Malone said. "I did not see or hear DeMarcus do anything from my vantage point that would have required a [first] technical foul to be called. And the ensuing one, I guess Scott Foster said he said a few choice words which warranted the second technical foul.
"Again, I did not see or hear anything for that first tech. That is something that we can look at and maybe speak to the league about, because from my vantage point, just didn't seem warranted."
Nuggets guard Will Barton offered his take.
"DeMarcus just has to be aware. He knows his reputation, and he knows that the slightest little thing is going to give him a technical foul," Barton said. "We have to talk to him and get him to understand that we can't have that. We just can't give them any extra points."
Cousins left with seven points, two rebounds, two assists and one block in 10 minutes.
The Warriors won 123-107 to take a 1-0 series lead.
A 12-year veteran, Cousins is in his first postseason with the Nuggets. He played for the Warriors during the 2018-19 season.