United, have lost three of their last six Premier League home games and is yet to win a competitive away game for the first time since March.
But Mata believes Solskjaer can turn the results around as they host Arsenal on Monday.
"I believe in him. I believe in how he really puts his life into the project that he's got in front of him." Mata told The Times. "He knew it was difficult when he came. He knows how our rivals are doing, but he wanted to take it anyway.
"The manager's position is sometimes exaggerated, for good and bad. Carlo Ancelotti won the Champions League with Real Madrid [in 2014], when they equalised in the 90th minute with the Sergio Ramos goal.
"If Luka Modric doesn't take the corner quick, and they lose? Is Ancelotti a worse manager? For me, no. I feel sorry for managers when I miss a chance, we lose and they get criticised and they did 'a bad plan'. It’s the same plan except I missed. It's me, not them.
"Of course, there are certain individuals that change a team: Diego Simeone, Jurgen Klopp, Pep [Guardiola]. Sir Alex [Ferguson] changed the history of this club. But sometimes we try to justify everything with the manager.
"Managers are very important but I like when I've heard Zinedine Zidane or Pep say, 'I'm good only because my players do the things I tell them to but I'm not the last connection with the ball'."
With Manchester United being able to keep hold of their star man Paul Pogba despite several offers from the big guns in Europe, Mata is happy the former Juventus man remained with the club.
"Paul is a very important player for us. He has fantastic qualities: physically, his vision's very good, his passing's very good," Mata added.
"He's a complete midfielder. He's got many things around him, social media life, but when you're face to face with him, he's very humble, a very nice guy, he has a good heart. I like him."
