Stand-in captain Mata curled home a set-piece from the edge of the area at Old Trafford as United claimed a fourth straight win in all competitions and earned back-to-back Premier League victories for the first time since November.
Van Gaal said an apparent knock prompted him to consider substituting Mata before his 83rd-minute winner.
"I am very happy he scored, he was captain today so it brings us luck I think," the Dutchman told Sky Sports.
"I was doubting between [Ander] Herrera and Mata but at the time we changed the positions of [Anthony] Martial and [Marcus] Rashford.
"Then we got that momentum again and Mata was limping also, so I wanted to change Herrera but then I saw that maybe Mata was injured.
"But it wasn't like that and I'm very happy I let him stay [on the pitch]."
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United are now level on points with neighbours Manchester City, who occupy the final Champions League qualification place but suffered a 3-0 defeat at Liverpool.
And, amid a heavy injury crisis, Van Gaal added: "I'm so happy for the players because the circumstances were not so good to play good football.
"It was more of a physical game and when you see how physical they [Watford] are - being twice the size of our players - I am very happy and very proud of my team.
"To beat Watford is a fantastic result and at the moment when your competitors are losing as well.
"It's fantastic but that's also the strength of the Premier League. We have lost to Sunderland and there was a lot of criticism but the difference between teams is not so big, so everyone can lose to anyone.
"When you win four games in a row you are always optimistic but we have a small group and a full programme. It's difficult."