The fans clearly put the blame on the Glazers and their chief executive Ed Woodward, more than manager Ole Gunnar Solskjaer.
Thousands of fans flooded out of Old Trafford well before the end of the game.
But the hardcore supporters in the Stretford End chose to stay and continue to make their feelings known.
“(In the) 84th minute I saw people get up and go. That is unheard of at this stadium.
“Seeing people leave with disdain on their face. It is an embarrassment.
“The downward spiral in seven years has been remarkable,” former Manchester United defender Rio Ferdinand said in his role as a match pundit for BT Sport.
The defeat leaves Manchester United fifth in the standings, six points adrift of Chelsea who currently occupy the fourth UEFA Champions League qualification spot.
Wood fired Burnley ahead in the 39th minute with a half-volley on the turn after a simple free-kick routine.
Ben Mee headed the ball down into the path of the New Zealand international.
The Clarets, who move up to 13th place, doubled their lead, seven minutes after the break, through striker Rodriguez who blasted into the top corner after a smart exchange with Wood.
Manchester United had a last minute header from Luke Shaw ruled out for pushing.
But they created few clear-cut chances as Burnley held on for their first victory at Old Trafford since 1962.
“It’s mad. It’s a great feeling. The lads have come in the dressing room buzzing,” said Burnley-born Rodriguez.
“These are the moments you work hard for. We stopped them playing. We showed our qualities to keep the ball and hurt them.
“That two-goal cushion was good for the team. This result means everything,” he added.
The Clarets, deserved winners, had drifted towards the relegation zone after four straight losses but this victory, following Sunday’s win over third-place Leicester City has steadied the ship.
