Michael Carrick and Kieran McKenna were keen for Manchester United to adopt a different style of play that was vetoed by former manager Ole Gunnar Solskjaer.
Caretaker manager Carrick and first-team coach McKenna wanted United to play with a back three sooner and arrest their porous defending.
Solskjaer had intended to change to a 4-3-3 formation in pre-season but United remained in a 4-2-3-1 until the 5-0 drubbing by Liverpool prompted a temporary switch to a back three against Tottenham, Atalanta and Manchester City.
United beat Tottenham 3-0 in the formation but abandoned it before half-time at Atalanta due to injury to Raphael Varane and changed to a back four for the second-half against City as they were 2-0 down.
In Carrick's first match in charge against Villarreal, United started in 4-2-3-1 but changed to 4-4-2 without the ball and 4-3-3 with it. Cristiano Ronaldo, Anthony Martial and Fred all changed roles throughout the 2-0 win.
Carrick and McKenna are responsible for training the players and there was widespread disbelief none of Solskjaer's backroom staff were sacked with him on Sunday.
Dressing room sources have said former Under-18 coach McKenna's methods are unpopular with a number of senior players and he has been described as a 'school teacher'.
United great Paul Scholes was staggered Solskjaer was the only coaching departure in the wake of the 4-1 thrashing by Watford and scathing of Carrick, McKenna, and assistant manager Mike Phelan.
"It's the same people running the team, it's the same people who had been given massive responsibility every single week to put that team on the pitch," Scholes told BT Sport ahead of the Villarreal tie. "Arguably, it's more Kieran McKenna and Michael Carrick who have been preparing the team. Ole gave them that responsibility to do that. So how that changes now, I don't know.