Mata became David Moyes' most high-profile signing at Old Trafford when he joined from Chelsea for £37.1 million last week.
The Spain midfielder made his debut for United in a 2-0 win over Cardiff City on Tuesday and will hope to lift his new club into the UEFA Champions League qualifying places from their current position of seventh.
Reflecting on Mata's arrival, Jones said: "It makes an impact in the dressing room when you sign a player of that calibre.
"He is such a talented player on the ball. He has definitely lifted spirits in the dressing room and especially in training.
"We want to impress and show him that we are one of the best teams to be at. He has done well and I am sure he will be a huge asset for us."
Mata, Chelsea's player of the year for the past two seasons, found himself marginalised at Stamford Bridge this term following Jose Mourinho's return.
Yet Jones said: "He will be a fantastic player for Manchester United.
"He sees the pass that sometimes no one else sees. If he continues to make them I am sure we will soon be climbing the table."
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