United were convincingly beaten by the Anfield outfit at Old Trafford, with Steven Gerrard scoring two penalties - and missing a third - before Luis Suarez secured the win, while Nemanja Vidic was sent off.
"The storm will pass and the sun will rise again," Mata wrote in his blog for Grada360. "I have no doubt. Besides, no one said this would be easy, but this is football.
"It gives you fantastic moments but also very hard times you have to cope with, when you have to show pride and professionalism until the end. And when all this is gone I’m sure I will be a more mature footballer.
"I have to say that our week at the training ground had been good and we were very hopeful ahead of this derby.
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United face Olympiakos in the Champions League at Old Trafford on Wednesday, hoping to overturn a two-goal deficit and advance to the quarter-finals.