The Baggies are preparing to take on a United side that looked to be close to hitting top form before the international break, and Irvine insists that his players cannot afford to gift possession to Louis van Gaal's team.
"We've done our video work and there are clips of them scoring goals where it starts with the goalkeeper and ends up in the back of the net," the West Brom boss told reporters. "Clearly that involves a lot of control and a lot of movement and good positioning of their players.
"We've got to be really well organised when we don't have the ball in order to stop them building these attacks.
"But one of the things we've spoken about is the need for us to be really good with the ball and not give it back really cheaply to players of the quality of Manchester United."
West Brom will draw level with United on 11 points if they can record a win on Monday.