The Spain international became the club's record signing when he moved from Chelsea for a fee of £37.1m and he impressed in United's 2-0 win over Cardiff on Tuesday night in his first match since his move.
United are 13 points behind local rivals Manchester City in the defence of their Premier League title, and have started 2014 with exits from the FA Cup and Capital One Cup but Jones is confident that Mata will bring out the best in the rest of David Moyes' squad.
"It makes an impact in the dressing room when you sign a player of that calibre," Jones declared. "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 what we are, 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 and fantastic player for Manchester United, hopefully for many years to come.
"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."
United's win over Cardiff featured Robin van Persie's first appearance following a thigh injury that had kept the Dutch striker sidelined since early December.
Wayne Rooney appeared off the bench having shaken off a groin problem, and Jones says that a shrinking injury list together with Mata's arrival has already lifted spirits.
"Robin has worked hard to get back," added Jones. "We are delighted to have him, Wazza and Juan now. Bar Marouane Fellaini and Michael Carrick, we will be at full strength on Saturday (at Stoke) hopefully,
"When you do miss players of that stature, you need to find it elsewhere. We are just delighted to get them back and firing again."