The Saints bounced back after going behind at Manchester United to earn a dramatic point last time out.
And boss Hasenhuttl believes their resilience is something they can continue to build on in the final three matches of the campaign.
“It says that we never stop believing and this is the difference now,” the Saints boss told the media when asked about his players’ mentality.
“In the not so good games we draw and in the good games, we win. This is a fantastic combination.
“Earlier we’ve drawn the good games and lost the bad ones. This next step is what we want to build on.”
Pressing provides rewards
Southampton earned praise for their ability to press at Old Trafford, with the opening goal coming after Danny Ings won possession high up the pitch.
Stuart Armstrong duly converted that opportunity, but only for Marcus Rashford and Anthony Martial goals to see United go into the interval in front.
Despite that, the Saints enjoyed the better of the second period and duly got their equaliser deep in stoppage time when Michael Obafemi turned in Jan Bednarek’s header.
Speaking about his side’s ability to press, Hasenhuttl said: “I think this is our way and the way we want to play.
“We want to control the game, even if we don’t have the ball. That’s the secret.
“If you have good management and you are flexible with the pressing then I think you can cause every club problems.
“We know we concede goals, but I think it’s getting better and better. We have fewer moments where we are less organised.”
Brighton provide the opposition for the Saints’ penultimate home game of the Premier League campaign, and whilst complimentary of his opposite number Graham Potter, Hasenhuttl made it clear that he wants all three points.
He said: “I really enjoy watching them play football. For me, in possession, he is one of the best managers in the league.
“You can see his signing on the team immediately when you see them play. The job he’s done since he’s been there is fantastic.
“He made a different way. I think this is maybe the reason why he is so focused on this playing with the ball.”
Having beaten the Seagulls 2-0 at the AMEX Stadium back in August, the Saints will be looking to complete the league double over their south-cost rivals.
Hasenhuttl added: “We want to take as many points as possible, and we don’t want to lose any more games. The results are good, the performance is good, and we can feel that we’ve made some steps.”
Whilst the Seagulls look to have done enough to avoid the drop, they will be keen to add to their points tally and victory for them would make it mathematically certain they will be playing top-flight football next season.