Van Gaal's fourth Premier League win lifted his team to sixth in the table but they struggled to break down a stubborn Palace defence despite dominating possession at Old Trafford.
Injuries and suspensions forced Van Gaal to field a makeshift central defence of Paddy McNair and Daley Blind and they enjoyed a relatively quiet afternoon against a toothless Palace attack.
"It was a fantastic goal but it was important also," Van Gaal told the BBC.
"It is always difficult to attack against a defending team, who comes here to defend and not attack. You have two rows of four and we created a lot of possibilities.
"I am pleased because we have three points and there is an international break so it was important we closed with a victory."
Mata came on as a second-half substitute for Adnan Januzaj and made an immediate impact before hitting the post late in the game.
"Juan Mata has played a lot of matches," Van Gaal said.
"I have given him the chance, I give other players the chance and at the end we shall see who plays more than the other. It is always like that in football."
United were without five first-choice defenders with Chris Smalling suspended and Phil Jones, Rafael, Jonny Evans and Marcos Rojo injured.
Versatile Dutchman Blind proved a competent partner for the 19-year-old McNair and Michael Carrick started in midfield alongside Marouane Fellaini following his recovery from injury.
"McNair and Blind didn't have to defend too much because we always had the ball," Van Gaal said.
"They only had to defend the long balls but that is difficult because (Marouane) Chamakh and (Fraizer) Campbell are strong headers of the ball."
It was another subdued performance from striker Robin van Persie, captain Wayne Rooney struggled to make an impact and record signing Angel di Maria was withdrawn in favour of young forward James Wilson 20 minutes from time.
Van Gaal will hope to get some defenders back for the trip to Arsenal on Nov. 22 but, after saying it might take three years to restore United to former glories, he has plenty to think about during the two-week international break. (Reporting by Ed Osmond, editing by Mark Meadows)
