Louis van Gaal's side had remained unbeaten throughout pre-season and had been expected to defeat their Welsh opponents on the opening day of the Premier League season at Old Trafford, but goals from Ki Sung-Yueng and Gylfi Sigurdsson secured all three points for Garry Monk's men.
Reflecting on that loss and looking ahead to upcoming encounters, Mata has urged his teammates to learn from their mistakes.
"We couldn't manage to show what we had been working on in previous days. Swansea had a very solid game and things got tough for us after their first goal," the Spaniard wrote in his blog.
"It was a big disappointment, that's the truth. We were hoping to make a good Premiership debut in Old Trafford, but it is also true that this is just the beginning. We need to set a regular pace and learn from our mistakes.
"In order to get to our goals, the goals this club and our supporters deserve, we know we have to be better than we were on Saturday. Anything you want to achieve, you need to put a lot of effort in it and that is what we are going to do. Learning from a bad result will make the team grow and move forward in this new stage."
Next weekend the Red Devils travel to the Stadium of Light for a clash with Sunderland.