The Premier League giants were unable to record a single shot on target during the whole game, and surrendered their 10-match unbeaten league run.
Dusan Tadic scored the only goal of the game after 69 minutes. Even though United reacted strongly they failed to find an equaliser, with Mata himself missing three good chances.
"They scored after the break in one of the few chances they had, after a ball that rebounded on the post, and then we tried everything to tie the game. I think we deserved that goal," Mata wrote in his weekly blog.
"In the last 20 minutes we had chances. I had three myself, but yesterday it seemed the ball just didn't want to go in. It would've been very important to take some of them because I believe we could have even won. I tried every possible way until the end, but we just couldn't make it. Next time it will be a different story, I'm sure."
Nevertheless, the Spaniard believes Louis van Gaal's side deserved at least a point as they controlled possession throughout the game.
"To be honest, I don't think we deserved to lose against Southampton. It was not the best game to watch. They were well positioned and defended very well, so creating chances was difficult. And yet we were in control of the game," he said.
"The first half was not very good; the game was quite slow, too tactical. But we kept the ball most of the time, trying to find spaces towards the goal."
United will visit QPR on Saturday (17 January) hoping to return to winning ways and consolidate their position in the Champions League places.
"Anyway, what matters now is to win our next game, regardless of who scores. We visit QPR and it's going to be a tough one. They are in need of points and we know we must go back to a good streak of wins."