United had lost their last four meetings with City but goals from Ashley Young, Marouane Fellaini, Mata and Chris Smalling gave the Red Devils their biggest derby win for six years.
Sergio Aguero opened the scoring and also netted late on for his 100th City goal but United were by far the better team to tighten their grip on third spot in the Barclays Premier League.
"The first 10 or 15 minutes they were brilliant and played well but after that the team showed character and we came back," Mata told Sky Sports 1.
"It's a massive win for us, it's a great result and everyone at United is happy.
"The atmosphere was crazy, it is something we will never forget.
"You could tell how important it was for the fans but we still have six games to go and we have to keep going.
"It's a big win and a boost of confidence but Arsenal are doing great and I'm sure City and Liverpool will fight to the end, so we have to fight to the last minute."
Young equalised Aguero's early strike and then set up Fellaini to give United a first-half lead
"We were disappointed to go a goal behind but we showed that team spirit to get back in the game and no other team was going to win it when we went ahead," Young told Sky Sports 1.
"It was an amazing feeling to score
I was delighted to put the ball in the net and get an assist as well but the important thing was we showed that character to win the game.
"It was a magnificent win
We knew it was going to be a tough game but we knew we had to get the three points."
United manager Louis van Gaal called the victory a "fantastic result" but criticised himself for leaving his side with 10 men following Michael Carrick's late injury.
"We are four points ahead of the fourth place in the table and I am very happy for the fans because I have seen what it meant to them when the results were not so good," Van Gaal told Sky Sports 1.
"It is a fantastic result and I must bring Carrick off the pitch at 4-1 because he was injured.
"It was a little bit stupid of me because I want to give all my players minutes who are working very hard.
"Some of my players did not know we had 10 men because the crowd was yelling.
"Wayne (Rooney) did know because he was the holding midfielder as did Ashley Young, but the rest was difficult."
Van Gaal's side have now won their last four league matches - against Tottenham, Liverpool, Aston Villa and Manchester City - since being knocked out of the FA Cup to Arsenal and a top-four spot and Champions League qualification now looks within their grasp.
"We have made big steps in the last six games but the defeat to Arsenal was very difficult for my team to stand up and maintain our confidence in the philosophy," Van Gaal said.
"But all credit to the players because they have to do it under the expectation of the fans.
"We started very badly and we were not the Manchester United we have seen in the last matches.
"I don't know why we were nervous but we could not get pressure on the ball in the beginning, but then we scored and from that moment there was more confidence in my team.
"We started to develop our pace and game plan and the second half was much better than the first half, and until the moment Michael goes off the pitch we were fantastic."
Manchester City manager Manuel Pellegrini fended off questions about his own future after an eighth defeat for his team in all competitions since the turn of the year.
"I don't think what happens to me is the most important thing," Pellegrini said.
"I will continue working and try to be as near as the top of the table as we can.
"We played very well for the first 20 minutes and had two or three more clear chances to score, but the moment they scored they grew and started playing better and we made mistakes for two of their goals.
"Maybe the third goal was offside and something similar happened in the last game but I'm not talking about referees."
Source : PA