United's seventh-place finish this season is their worst in the Premier League era and means they will be absent from European competition for the first time in 25 years.
However, Mata has vowed to put that right after ending the campaign by scoring United's equaliser in the 1-1 draw at Southampton on Sunday.
"It's always nice to finish with a goal, and especially from a free-kick," said the Spaniard.
"I will tell David De Gea to stay with me at the end of the training sessions so I can practise more.
"The goal helped the team to avoid a defeat in Southampton, although the score and our final position on the table is nothing we feel proud of.
"At United, if you don't win the Premier League one year you know you have to do it the next time, and we will get ready for that.
"I believe it's fair to congratulate Manchester City for winning for the title. We will try to bring the celebrations to our side the next year."
The 26-year-old has won the club's player of the month award in two of the three months since his arrival from Chelsea and is "looking forward to more".
But it was his compatriot David de Gea who collected the Player of the Year award - becoming the first goalkeeper to win it.
"The big prize was for De Gea and I was honoured to present it: United's Player of the Year, voted for both by the fans and the players," he posted on his official website, www.juanmata10.com.
"It's the first time that the trophy goes to a United goalkeeper and David deserves a lot of credit for that.
"He's got amazing qualities and he may become one of the best goalkeepers in the world - I believe so."