Meetings between the two arch-enemies are always lively affairs, and their latest rekindling of the old rivalry at Old Trafford proved to be no different.
The visitors took the lead from the penalty spot in the first half, with James Milner making Paul Pogba pay for a baffling handling of the ball inside the box.
Both sides then squandered chances before Zlatan Ibrahimovic restored parity six minutes from time.
United were firmly on the front foot by that stage and Mata believes they would have grabbed a second goal and all three points had stoppage-time been extended a little further.
He wrote in a blog on his personal website: “Liverpool scored first, from the penalty spot, and we couldn’t take our chances to equalise before the break.
“In the last few minutes we pushed really hard for the victory, which is something that United has done for many years in the past.
“Zlatan was able to tie the score, and we felt that, if the game had lasted a big longer, we would’ve won. It was a pity, because our goal was the three points, obviously.
“Perhaps we didn’t see the best football but it was a thrilling game full of rivalry.
“All we have to think about now is starting over and trying to win the next game. The team showed pride until the end, and Old Trafford fought with us, as always.”
United are next in action away at Stoke City on Saturday.