Ferguson remains in intensive care two days after undergoing emergency surgery for a brain haemorrhage, which a Red Devils statement confirmed had "gone very well".
In a difficult week for all associated to United, Mata has set his sights on making the legendary Old Trafford boss proud by instilling some of the fighting spirit that made the Scotsman so successful.
"All of us were overwhelmed by the news about Sir Alex Ferguson's health condition. This circumstance has had a huge impact on Manchester United, as you can imagine," he wrote on his personal blog.
"All of us are united right now, wishing Sir Alex a speedy recovery. He has been a unique and fundamental figure in the football world over the last few decades.
"I've never been coached by him, unfortunately, yet I know well his incomparable legacy on this club, that winning mentality and fight that we must honour in the last three games of the season, especially in the FA Cup final. To achieve that, we are going to work hard while we eagerly await good news about Sir Alex's recovery."
United have league games against West Ham United and Watford before facing Chelsea in the final on May 19.