Veteran midfielder Robbie Blake was the match winner, lashing home an 18th-minute volley after a period of Burnley pressure.
Related ArticlesBurnley 1 Manchester United 0Burnley's old-fashioned wayBurnley v Manchester Utd previewBurnley lacking defendersBurnley warm to Premier battleBut goalkeeper Brian Jensen also deserved hero status, saving Michael Carrick's penalty just before half-time to lay the platform for an unexpected triumph, repeating Carling Cup shoot-out heroics from last season.
"I have told the players to enjoy it because it is not often you beat Manchester United," said Coyle.
"I felt before the game if everything went our way we could probably get a positive result.
"Then I saw a statistic on TV that Manchester United had won their last 17 matches against newly-promoted teams, scored 44 and conceded four. At that point I wish the TV had been turned off.
"We rode our luck at times but we offered enough of a goal threat. The goal itself was outstanding, although I was not surprised because that is the type of thing he has in his locker."
It was the perfect response to Saturday's 2-0 defeat at Stoke.
That reverse had the critics out in force, claiming there was no way Burnley, with their minuscule budget, could possibly survive in such rareified company.
"One or two have already written us off," said Coyle.
"I am not surprised about that. When you look at the financial side, we will have to produce every week.
"Outside this club, everybody looked at our first five games (Stoke, United, Everton, Chelsea and Liverpool) and expected we would be on zero points.
"We were disappointed on Sunday and we needed to be brave tonight. Now we have a massive game on Sunday against Everton, although whatever happens we are three points better off than we were at this stage in the Championship last season."
Sir Alex Ferguson was quick to offer congratulations to his fellow countryman, whose reputation is growing almost by the week.
And Ferguson is no doubt relieved his side will not encounter many atmospheres as hostile as the one United experienced tonight.
"People refer to this as a ramshackle place but I love this type of stadium," said Coyle.
"And the supporters know that these players will give their maximum in every game.
"Sir Alex said well done at the end. He dealt with defeat in the gracious manner I would expect of someone like that.
"He is the best manager in world football and I still expect Manchester United to be champions."
Ferguson could do little other than accept his side had got what they deserved.
"It was a bad performance considering the chances we had and the possession we had," he said.
"In fairness to Burnley they caused us problems and had a good spell in the first half.
"It has been a long time for them out of the top flight and you cannot deny them their victory.
"They have worked hard and the fans have been fantastic.
"They got behind them all night with everybody kicking the ball. It was fantastic for them on their return. It was a great occasion for them."
The choice of Carrick as a penalty-taker ahead of Rooney and Owen, who wasted two excellent chances in front of England coach Fabio Capello, was a surprise.
"Maybe if we had got the penalty just before half time it would have made a difference but in saying that we were too frivolous with the chances we had," he said.
United now head to Wigan on Saturday knowing they already have ground to make up in their bid to land an unprecedented fourth successive league title.
"I am sure we will get a response at Wigan," said Ferguson.
"The players are all disappointed. It was a bad result for us. It was a good passing pitch and we should have done better."