In-form Saints significantly eased Premier League relegation fears during a productive festive period which brought 10 points from a possible 12 and statement victories over Chelsea and Tottenham.
The south coast club on Saturday travel to Brendan Rodgers' second-placed Foxes bidding to banish bitter memories of October's record-breaking embarrassment on home soil.
Saints manager Hasenhuttl feels recent results have boosted morale among his squad and has seen no signs of complacency as their quest for top-flight survival continues.
"When you get good results you can feel also in the sessions that the quality is rising and the self-confidence is rising and the belief is back," said the Austrian.
"When you have clean sheets against Tottenham and Chelsea and win, then it feels fantastic for the players.
"But I still don't have the feeling that they are not hungry anymore, so we stay on hunting and we know that it's only short-term where we took a lot of points.
"I don't see the reason why we should stop or lean back now because this is an important period of the season and the more points you take now, the less pressure you have in the end.
"We did it fantastic so far but we are still way off being in a comfort zone – we don't want to be."
Southampton's remarkable revival has seen them climb to 12th place in the table, five points clear of the bottom three.
Their impressive form included a surprise 2-0 Boxing Day success at Stamford Bridge and a battling 1-0 home victory over Jose Mourinho's Spurs on New Year's Day.
Seventeen of the club's 25 points this season have come from their 11 fixtures since Leicester ran riot at St Mary's little more than two months ago.
The 9-0 drubbing was the worst defeat in the club's 134-year existence and the heaviest home loss in top-flight history. It also equalled Ipswich's 1995 thrashing by Manchester United as the biggest defeat of the Premier League era.
Despite being on the receiving end in dramatic fashion, Hasenhuttl admits to being impressed by the work done by Rodgers at the King Power Stadium.
"It's a very strong side. He does a fantastic job with his team," he said.
"They have a clear philosophy and are very flexible in their shape – not a coincidence that they are so high in the table.
"To take something against them, it's not so easy. But we want to show we can do it better than the first game."