Anthony Martial and Paul Pogba struck in the closing minutes to hand United a deserved three points against Boro at Old Trafford.
“I don’t like to lose, but I think the performance, once again against a top team, was really good,” said the Spaniard.
“When you score at the time that we did and you lose, it is difficult to take, but we have to take the good things from the game.
“Once again we competed well with a top side who win only in the last five minutes. I’m pleased with the way we competed and we will win games against teams who are playing to stay in the Premier League.
“We have come to Manchester United and they have to finish the game with Ibrahimovic, Pogba, (Henrikh) Mkhitaryan, Martial, (Marcus) Rashford all on the pitch.
“My players have to forget the result and keep the performance. They can be very proud.”
United dominated the 90 minutes, raining 32 efforts down on the Boro goal, but were denied twice by the woodwork, once by a contentious refereeing decision and on multiple occasions by their former goalkeeper Victor Valdes.
When Grant Leadbitter lashed home his first Premier League goal in almost eight years it looked as though a scarcely believable upset was on the cards, but Martial and Pogba found the net in quick succession during a frantic last five minutes to seal a win. It left United boasting a six-game winning streak heading into 2017.
The Red Devils were fine value for the points with both goalscorers hitting the woodwork previously and Zlatan Ibrahimovic unfortunate to see his kung-fu style finish ruled out for high feet.
Manchester United: de Gea, Valencia, Bailly, Smalling (Rashford 72), Blind (Rojo 64), Fellaini (Mata 64), Ander Herrera, Pogba, Mkhitaryan, Ibrahimovic, Martial. Unused substitutes: Jones, Lingard, Romero, Schweinsteiger.
Middlesbrough: Valdes, Chambers, Bernardo, Gibson, Friend, de Roon, Traore (Da Silva 82), Forshaw, Leadbitter (Clayton 78), Downing (Ramirez 63), Negredo. Unused substitutes: Ayala, Rhodes, Guzan, Stuani.
Referee: Lee Mason (Lancashire).