Saints sit 11th in the Premier League table.
Southampton manager Ralph Hasenhuttl accepts key players will continue to leave St Mary’s, despite the club’s recent takeover.
Saints looked destined for a season of struggle after star striker Danny Ings was sold to Premier League rivals Aston Villa for around £26million last summer.
But, having gone seven top-flight games without success at the start of the campaign, Hasenhuttl’s men moved 13 points clear of the relegation zone – and above Villa – courtesy of Tuesday’s thumping 4-1 success over Brentford.
New owners Sport Republic last week bought an 80 per cent stake in the club and were in the stands to watch an emphatic start to the new era on home soil following Saturday’s behind-closed-doors FA Cup win at Swansea.
The arrival of the Dragan Solak-backed investment firm should allow Saints to move more quickly in the transfer market but Hasenhuttl admits it will remain difficult to keep hold of top talent.
“Yes, it is tough if you lose players in the summer, it is tough if you lose your top scorer,” said the Austrian.
“It takes a bit of time to build up a new team but this is the job you have to do if you want to be the manager of this club, because it will also happen in the future.
“This is normal in football, especially for us as a club.
“With all the promise we had after every season and then we lose our best players, you have to start again and again and again.
“But this is the way you have to work and – in the end – when you have the patience and the passion for this club, then you know that you’ll come back.
“It’s important that you keep on going and keep on finding solutions.”
Jan Bednarek headed Southampton in front against the Bees before an own goal from visiting goalkeeper Alvaro Fernandez restored the lead after Vitaly Janelt briefly levelled with a fine volley.
Second-half strikes from Armando Broja and substitute Che Adams sealed a deserved victory for the rampant hosts.
Chelsea loanee Broja now has five league goals for the season following an unconvincing start to his temporary spell with Saints.
Hasenhuttl is eager to keep the 20-year-old Albania international beyond the end of the current campaign.
“Yeah, sure, I mean he likes it here, he loves it here, it would be great if he’s our player,” said Hasenhuttl.
“He wants to be here with us, you can feel this at every moment. The fans love him. It’s good.”
Broja – who raced away from halfway before slotting beyond Bees goalkeeper Fernandez just after the break – echoed his manager’s words.
“I’m loving my football so far here at St Mary’s,” he told the club website. “I’m just buzzing.
“It’s just a really amazing moment for me and my family and I’m just really thankful for this opportunity.
“I’m not going to get too carried away, I’m just going to keep going.”
Lacklustre Brentford were leapfrogged in the table by their opponents following a disappointing display.
Bees manager Thomas Frank apologised to the travelling fans and urged his players to swiftly move on ahead of a weekend trip to Liverpool followed by the visit of Manchester United.
“We can’t feel sorry for ourselves, because there’s a big task ahead of us on Sunday,” said Frank.
“(There) was definitely a lot to learn. We need to be better on the ball and better on the second balls.”
Speaking about the sold-out away end, the Dane added: “(It was a) full support, maximum capacity. I’m sorry we couldn’t do better.”
