Boos rang around Old Trafford following the final whistle of the Barclays Premier League contest as United boss Louis van Gaal endured what he later described as the worst reaction he has heard from supporters yet during his time in charge.
The Red Devils - frequently derided of late for playing in a dull, uninspiring way - had just one shot on target in a match that was settled by Charlie Austin's late header.
They are now five points off the top four in fifth place and have won only three of their last 13 matches in all competitions.
Van Gaal has expressed his own frustration, saying: "I'm very disappointed that I cannot reach the expectations of the fans.
"They have - or they had - great expectations of me, and I cannot fulfil them."
Meanwhile, Mata - who came on as a half-time substitute in the defeat - said in a message posted on his blog on Monday: "Once again I'm writing with a bad taste.
"After several games without being defeated, we lost 0-1 to Southampton in Old Trafford. And it hurts, it really does.
"It was the perfect time to get the three points and stretch the good streak in 2016, but we couldn't make it.
"It wasn't a good game from any of the teams, a draw would have been a fair result (although not good enough for us), but a late goal from Austin after a free-kick took the points away from us.
"It's another tough moment, for you and for us, but we must get through this. I understand your frustration, because we feel the same way, but we have to carry on."
Mata has no doubt results must improve.
United's next match is an FA Cup tie at Derby on Friday, and the Spain international added in his message to the fans: "Football doesn't stop and now it's time for the FA Cup and we want to fight for this trophy for you.
"We feel bad every time we get a bad result, but it hurts even more for you.
"We must get better results for you.
"I thank you for your support in the bad times, and I assure you that our only goal is to do things much better to move up the table in the Premier League and try to lift the FA Cup.
"Thanks to all of you. I'm sure that better moments will come sooner or later, and we will enjoy them much more, aware of how tough it is to get there."
Van Gaal and his players have had both Sunday and Monday off - as was always scheduled - and are due to return to work on Tuesday.