The former RB Leipzig boss was announced as successor to Mark Hughes before the game and watched as goals from Harry Kane, Lucas Moura and Son Heung-min condemned Saints to their eighth league defeat of the season.
Despite the loss, caretaker manager Kelvin Davis said the Austrian would be inheriting a talented, if underperforming, squad when he officially takes charge on Thursday.
"I think we’ve got a good set of players, an honest set of players," Davis told a news conference.
"I think it’s a mindset (problem) not confidence. If you look at the goals we conceded they are goals that are, ultimately, easy to stop.
"It’s a mindset thing and I think confidence will build from that. It’s not a group that mentally isn’t in a good place."
Hasenhuettl made waves in Germany by guiding newly-promoted Leipzig to second place in the Bundesliga in the 2016-17 season before leaving last May after a dispute over a new contract.
Davis believes that in Hasenhuettl, Southampton have finally found the right man for the job.
"We met at the hotel after lunch and he was very concise with his information, very honest, very to the point on what he wanted and explained how he wants to work," said Davis, who will continue to work as an assistant coach.
"He’s generally got a good feel to him, he's very keen to come in and improve us as a group and the fact he wants to join our football club is fantastic with the pedigree he's got. He's really looking forward to getting started."
Hasenhuettl does not have much time to prepare for his first match as it comes at Cardiff City on Saturday. A win would not only be a significant morale booster but would also be likely to lift the 18th-place side out of the bottom three. (Reporting by Christian Radnedge Editing by Nick Mulvenney)
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