United's involvement in both the FA Cup and Europa League as well as the Premier League has seen them play three times in the last seven days, with the clash against managerless Boro coming up at 12:00 GMT on Sunday.
The Red Devils are likely to be without both Paul Pogba and Daley Blind, who both picked up injuries in Thursday's win over Rostov, while Zlatan Ibrahimovic and Ander Herrera are suspended.
And Mourinho believes fatigue has played its part in the fitness levels of his squad, leaving them facing an uphill task at the Riverside Stadium.
"It's difficult to play Monday with 10 men, it's difficult to play now, it's difficult to play 12 o’clock on Sunday. We have a lot of enemies," he told BT Sport.
"A lot of people might say we should have scored more goals. But a lot of things are going against us.
"The boys are amazing boys. We will probably lose the game on Sunday. Fatigue has a price.
"I will remember forever when I spoke to the UEFA delegate in Rostov. He told me if any of our players gets injured, the insurance paid.
"Whoever decided the Monday and Sunday games probably thinks the same way.”
United will find out their opponents in the quarter-finals of the Europa League on Friday, with the draw taking place at 12:00 GMT.