Sunday's 3-0 loss at Old Trafford stood out not only for the visitors underlining their credentials as Premier League title challengers, but also United's inability to compete against their north-west rivals.
But even after the final whistle, large pockets of supporters remained to voice their support for the team and Mata said he was disappointed the players could not match that level of performance.
"There are no words to describe your support in the stadium," he wrote in his personal online blog.
"In games like yesterday it makes me mad not being able to give you what you deserve.
"I know there is nothing I can say right now but at least I want you to know how I feel."
Mata joined United from Chelsea in January for £38million but there has been no vast improvement in results, with just three wins from the seven matches he has been involved in, being ineligible for the Champions League defeat to Olympiacos.
However, the 25-year-old believes the experience will make him a better player.
"The storm will pass and the sun will rise again. I have no doubt," said Mata.
"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."
United striker Wayne Rooney described the defeat to Liverpool as one of the darkest days of his career.
"It's one of the worst days I've ever had in football," Rooney told MUTV.
"It's hard to take. You have to give Liverpool credit - they played well - but it's difficult to take. Nobody wants to lose, especially in this way, in your own stadium. It's not nice."
Manager David Moyes admits his first season at Old Trafford after succeeding Sir Alex Ferguson is harder than he ever imagined.
"The job was always going to be hard. Harder? Yes I would say so yes," said the Scot, who has not given up hope of finishing in the top four despite being 12 points adrift of Manchester City, who have two matches in hand.
"It will be very difficult but it's not over yet, so we have to keep working as hard as we can towards trying to do it.
"I've been saying for a while we've given ourselves a long task and a long road to try to get back in it."