With the Spanish playmaker starting his fourth consecutive game on the bench, United took the lead after his compatriot Ander Herrera scored a great low striker in the 28th minute.
However, Swansea reacted with goals from Ki Sung-yueng and Bafetimbi Gomis, condemning United to their second Premier League defeat since November.
The £37.1m ($57m) Spanish maestro has not started a game since scoring the opener in the FA Cup 3-0 victory over Cambridge United on 3 February, with him being an unused substitute against West Ham, Burnley and Preston North End. And he only had 11 minutes to prove his worth by replacing Angel Di Maria during the defeat against Swansea.
Mata has expressed his frustration due to the result but refused to comment on his personal situation.
"As you can imagine, especially those who read this blog week after week, this is one of those days when writing is a bit complicated, following a tough defeat," the Spaniard wrote in his weekly blog.
"The week had had a good start, winning in the FA Cup and getting to the next round - when we will be facing Arsenal - but did not finish the way we expected."
Nevertheless, the Spaniard claimed United created enough chances to get a victory.
"I honestly think we were close to bring home the three points, especially because the feelings on the pitch at the start of the second half were good," he wrote.
"We played almost all the time in Swansea's half of the pitch, but we weren't able to take any chance and we all know that football can be capricious. We were ahead after a great goal from Ander in the first half, but were defeated later on with a lucky goal from Gomis after Shelvey's shot."
"Sometimes you win games that you don't deserve to win, and some other times, and I think this is the case, you just don't get what you deserve... This is football!"
The Spaniard urged his side to move on ahead of the forthcoming game against Sunderland in order to keep pushing for the Champions League places.
He wrote: "Now we must stand up again, look ahead and make it up to our fans the next weekend in Old Trafford against Sunderland. As I keep saying every week, and now even more, it is vital to win games. Our main rivals don't slow down and the race for the Champions League spots is closer than ever. We are approaching the most important moment of the season and we must deliver in order to get our goals."