Coach Francois Ciccolini, team manager Sonny Anderson and the rest of the staff, appointed in June, were dismissed immediately after a 2-0 loss at champions FC Basel left them pointless and goalless at the bottom of the league after two games.
"They can't ask us to perform magic," Ciccolini told the online edition of 20 Minutes newspaper.
Anderson added: "He [Chagaev] is the chief shareholder, he makes the decisions."
The club could not be reached for comment.
Neuchatel have already fired two coaches, ditched all their sponsors and sacked their administrative staff since Chagaev (pictured, left) took control in May, saying he wanted to lead them into the Champions League.
On Friday, they sacked Brazilian goalkeeper Rodrigo Galatto after only one week and one game at the club following his performance in a 3-0 home defeat by FC Lucerne in their opening match of the season.
NEWS:Neuchatel fire goalkeeper after one match
His replacement Jean-Francois Bedenik had to pick the ball out of the net after just 83 seconds as Benjamin Huggel put the hosts ahead in Sunday's game.
Gilles Binya scored an own goal 10 minutes before half-time as Basel strolled to an easy win.
Neucahtel fired coach Didier Olle-Nicole on May 12, the day the club was sold to Chagaev, and his replacement Bernard Challendes was dismissed three weeks later after the team escaped relegation but lost to Sion in the Swiss Cup final.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.