"But we need to keep going and, from (Christmas Eve), rest and think about the next game - obviously with the will of finishing the game with a much better feeling."
United's players looked ashen-faced as they traipsed onto the bus at Leicester, where they were on course for a comeback win after Mata's first top-flight brace since March 2015 cancelled out Jamie Vardy's opener.
The visitors had a number of chances to put the game to bed, but a lack of killer instinct - an all common theme last season - cost them maximum points.
Mourinho criticised his side's "childish" display after what felt like a pre-Christmas defeat for United.
"We didn't kill it - and we should have killed it," Mata said. "It's easy to say now.
"If we instead of drawing win at the end, we would have been saying that it was a fantastic game, that we came back and we did the most difficult thing which is to score twice after they went ahead.
"But that's football, you know, and in the last second they put the ball into the box and they scored.
"But we have the feeling that we should have killed the game before.
"It feels like a defeat. We get a point but it feels like a defeat because we were so close to winning and we had a chance to kill the game.
"They were with one less player (after Daniel Amartey was sent off) so it feels like a defeat."
United will still be without a string of first-team players as they look to get back to winning ways.
Michael Carrick and Maroaune Fellaini have been ruled out of the festive period, while Antonio Valencia has been struggling with a hamstring injury of late.
Eric Bailly is sidelined after ankle surgery and an unspecified injury meant versatile full-back Matteo Darmian missed the draw at Leicester, where Chris Smalling received a knock late in proceedings.
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Manchester United salvaged a point against Burnley thanks to Jesse Lingard.
Jose Mourinho's men were 2-0 down at half time and two goals from substitute Lingard earned a point, but it is another disappointing result for United.
Paul Pogba and Luke Shaw started but Chris Smalling, Anthony Martial and Antonio Valencia missed out through injury.
Zlatan Ibrahimovic also started but his partnership with Romelu Lukaku was far from a success and the Swede was hooked at half time.
United were behind within three minutes to an Ashley Barnes strike and matters were made worse when Steven Defour netted with a free kick midway through the first half.
Mourinho took drastic action at the break by bringing on Lingard and Henrikh Mkhitaryan for Ibrahimovic and Marcos Rojo.
Lingard proved his worth again but United were unable to find a crucial third goal to earn all three points and will hope for better against Southampton on Saturday.
MANCHESTER UNITED are desperate to put some pressure on rivals City at the top of the table.
But they won't have it easy as they welcome a Burnley side who have beaten Chelsea away and drawn at Liverpool and Tottenham.
