Junior Firpo’s second-half goal stopped Leeds’ 10-game winless run in the Premier League and took them out of the last three.
Gracia, a former Watford, Malaga and Valencia boss, was delighted with his winning start after being appointed as Jesse March’s permanent replacement on Tuesday.
The 52-year-old Spaniard said: “(I am) very happy because when I arrived I could feel that all the people at the club really needed a good result.
“Today I think it is good for the confidence of all of us. We know it’s just a step, but for us right now it’s an important step.”
Leeds slipped into the bottom three for the first time this season after a poor display in a 1-0 loss to Everton last week.
Firpo’s first top-flight goal for Leeds, a low shot past Southampton goalkeeper Gavin Bazunu in the 77th minute, secured their first league win since early November.
“I think this victory is good for the confidence of the players, in the work that we are going to do together and the confidence of all the fans in the team”, said Gracia.
“We know it’s just one win, just three points, but it’s something really special for us.”
The home fans in a crowd of 36,641 played their part as Leeds finally found the breakthrough against stubborn opponents, who remain last despite being boosted by victory at Chelsea the week before.
When asked about the atmosphere at Elland Road, Gracia added: “Really special. I knew because I could see before I came, but living inside is different.
“I am very optimistic because with a day that we play like today, next week we will play much better.”
Southampton confirmed caretaker boss Ruben Selles as permanent manager until the end of the season this week after recently sacking Nathan Jones.
The Saints responded with a morale-boosting 1-0 win against Chelsea in Selles’ first game in charge before falling to this 16th league defeat of the season.
It was the tenth time they had lost a league game by one goal and Selles insisted that his team was playing at “Premier League level”.
The 39-year-old said: “For me, it shows that we are there. We are present in every game and we have the possibility to act and win the game.
“We are not a team that is conceding a lot and is offside and therefore does not compete.
“We are competing. We are there and we are at the level of the Premier League. We are doing things and performing at that level”.