The former PSG midfielder made the switch to United on deadline day.
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With Uruguay for their World Cup qualifiers this week, Ugarte said after the draw with Paraguay: "It was very difficult and complicated because I tried not to live it with a lot of anxiety.
"But it was difficult. The pre-season was strange for me because I was not used to finding myself in this situation and playing so little. But now that everything has been resolved, I am very happy and I felt good on the pitch today.
"The wait was long and I was anxious at times. But this kind of situation happens to any player."