Mauricio Pellegrino confirmed Southampton hope to sign Arsenal's Theo Walcott this month after watching his team progress to the fourth round of the FA Cup with a 1-0 defeat of Fulham.
James Ward-Prowse's first-half finish at Craven Cottage ensured they ended a run of nine games without victory and eased the pressure building on their manager.
The club's supporters on Tuesday chanted for his dismissal when they fell to 17th in the Premier League by losing 2-1 to Crystal Palace.
At Fulham when he replaced Pierre-Emile Hojbjerg with Mario Lemina as Saints sought to preserve their narrow lead they sang, "You don't know what you're doing," but Pellegrino insists victory has given them a platform to build upon.
Following the £75 million sale of Virgil van Dijk to Liverpool, Southampton plan to strengthen their attacking options.
They remain uncertain about their hopes of re-signing Walcott, who left in 2006, but the manager said: "I have been talking about him.
"He is a good player, but I don't know with the negotiations, with the market. I imagine that this type of player would have a lot of possibility. For us it's not easy.
"Hopefully we can bring somebody that can help us be stronger. This is our target now. We know the market is difficult, but we are working on that."
Asked about the response from the visiting supporters to his 80th-minute decision to replace Hojbjerg, he said: "When I make a change I think it is best for the team. When the opponent is dominating, you need fresh players.
"I am not upset. I think the fans are with us and the team and were great from beginning until the end and I cannot complain about anything.
"I understand when the fans have their opinions, but when I am doing something I am thinking about my team and my players and not the fans.
"It is an important result for us and we have taken a step forward in this competition, and can hopefully use this game as a base to improve every single week."
The result ended Fulham's run of four successive home victories, and could have been by a wider margin after Jack Stephens headed against the crossbar, regardless of Denis Odoi's late miss.
"It was 50-50 at the end," Fulham boss Slavisa Jokanovic said. "They showed in one situation some Premier League quality, they scored the goal, they won the game. My team tried to dominate the game with the ball. They get to the next round.
"You always need to score to win the game. We played against a Premier League team, we must be clinical in some moments. We didn't make more of what we made, but in one moment they showed the quality and won the game.
"We are where we are. In this moment for us this competition is over, and we look at the next step."