"I was looking for the team to compete hard every night," said Dumars, a two-time NBA champion as a player who was hired in April by the Pelicans.
"If we start losing the same way over and over again, that's not improvement.
"Before you can become anything in this league, you have to establish that first as a team. It was that judgment (that led to a change) more than identity, more than the offence or defence, or the won-loss record," Dumars said in comments posted on the Pelicans website.
The Pelicans started the season 0-6 as they dealt with injuries to key players. Star big man Zion Williamson has played just five games because of a hamstring injury - a problem that has hindered him in four straight campaigns.
Jordan Poole missed games with a quadriceps strain, and Dejounte Murray is still recovering from a torn Achilles tendon suffered last January.
New Orleans lost three of their first six games by at least 30 points and allowed at least 120 points in five straight games to start the season.
A 118-104 loss to the Los Angeles Lakers on Friday was their fourth straight defeat.
Assistant James Borrego will take over as interim coach. Borrego, the former head coach of the Charlotte Hornets, was considered for head coaching jobs with the Lakers and Cleveland Cavaliers in 2024.
Dumars said he expected Borrego to be at the helm for the remainder of the season.